This is obviously a sequel to this post, this other post about how non-weapon equipment and its mechanics can influence a game, and this third, fourth and fifth post about distribution of tech amongst the general population.
I can't entirely avoid talking about this stuff again, but it's a different angle.
What kind of weapons are commonly available to civilians is a huge deal. There's a complex mixture of legality, opportunity and culture here, but I don't claim to understand that.
One factor is the typical discrepancy between a civilian and a ne'erdowell. If armed civilians tend to carry the same level of weaponry as a criminal, it's more likely civilians will tackle criminals. This also makes it harder to pick out a likely threat from a crowd, be they would-be assassins or the police you're trying to avoid; you can't simply scan to see who's armed and focus on them.
How often people carry weapons is another factor. If everyone's armed, you need to bear in mind that nobody is a negligible threat, especially once firearms come into the picture. Any crowd of civilians might be a serious problem, either under the sinister influence of psychic aliens, or because they think you're a criminal. Moreover, there's a good chance that anyone who discovers you doing something weird will confront you, rather than cowering or fleeing. Of course, if civilians carry knives while you have a flamethrower, this is less likely (see above).
A sort-of-separate point is that the salience of a weapon depends on the weapon culture. Can you determine anything about a person based on what they carry? If weapons are outlawed, an armed person is either law enforcement, military or a criminal. Some weapons may be restricted by social class, or licence - the fact that this person can afford the extortionate null-weapon licence is significant, especially if they look like a nobody.
In our case, a lot of this stuff is going to vary by planetary culture, but the broad level of technology is still important. Some important weapon technologies are: firearms, computerised weaponry, stunners, radiation weaponry, indirect weaponry like gas or seeking ammo.
Firearms are important because their power is largely independent of the wielder. The overall threat they pose is still very variable, but they simply aren't wielder-dependent in the same way as a club or bow. A competent fighter has little to fear from a novice with a sword, and a child with a bow is irrelevant - probably can't even loose the arrow properly. A toddler with a handgun can do exactly as much damage to a veteran special forces operative as another VSFO could, and is far more unpredictable. At short range, even marksmanship doesn't matter much.
So, if firearms are widespread, a character in a dangerous situation must beware of anyone who gets close to them. Automatic weapons, and similar things, simply offer massive damage output far beyond what any individual could do otherwise. This allows one wielder to pose a serious threat to a far greater number, without setting up an elaborate scheme to gain advantage. Suppressive fire and similar effects are also relevant. Intelligent weaponry that can work or aim by itself is essentially the same issue as software, discussed above: a person gains capabilities far beyond what their body offers.
Stun technology is important because it has low consequences, and so is used more freely. Police forces around the world are cheerfully tasering people they would (at least in Britain) have never got away with shooting. Stun technology that was genuinely non-lethal would be even more freely used. Criminals would use them to safely rob people: muggers, housebreakers, bank robbers, just walk in and stun away. Civilians would use them on suspicious persons, because you have much less to be concerned about in terms of guilt or legal consequence if you make a mistake. Troublemakers would use it to wreak havoc, just like they drop binbags off road bridges, or push bikers into rivers.
If you start thinking about what portable stunner technology as depicted in sci-fi could lead to, it's a bit terrifying. For example: it doesn't matter how non-lethal your weapon is if your target is driving a petrol tanker on the motorway.
Radiation weaponry, or whatever other technobabble you like, allows weapons to affect a target through solid objects. This is a game-changer in terms of line of effect, especially as it's probably paired with technology to partly see through said objects. Diving for cover is ineffective. A guard outside a building remains a threat even once you're safely inside. A character with a rad weapon can sit inside a bunker or vehicle and safely take down large numbers of targets, if they don't have such equipment. This sort of technology should affect the approaches taken by military or law enforcement, the equipment they carry, and the protection they need.
Indirect weaponry is very similar so I'll shut up.
Armour is generally a distant second to weaponry because it's inconvenient, but the availability of armour is important. The biggest reason is that it affects low-level antagonists.
You can generally expect that a military droid, or the leader of an armed rebellion, will have some armour. Law enforcement typically have some level of armour too - even ordinary bobbies wear stab vests. But the tech level of armour is important. If tough, comfortable armour is easy to manufacture, then the bobby could easily shrug off bullets (apart from that awkward head region). This makes a police officer or security guard a bigger potential threat to a PC, but also changes their role. Often ordinary law enforcement can seem little better than hapless civilians, in need of protection by the big tough PCs, and it's practically murder to call them in when an antagonist arrives. Once they're armoured up, though, they are better able to take care of themselves. The officer confronting the villain becomes a mild asset rather than a liability (or distraction), and calling in the scuffers to handle a situation isn't inviting a massacre.
Taking that further, forget capability and think about availability. How easy is it to get your hands on that bonded polycarbide armour? Two of the reasons criminals tend not to wear armour are, it's difficult to get hold of, and it's really uncomfortable and obvious. Once bulletsilk undershirts are readily available, every two-bit thug might as well wear one and cut down the risk of buying the farm if something kicks off. You can certainly bet that anyone who planned a crime is likely to wear armour, once it gets to the point that you can do so unobtrusively. The bank heist or break-in will be a lot safer if you're nearly bulletproof.
This step elevates the difficulty of defeating, oh, civilian threats, if you like. I feel like this will somewhat change the balance (mechanical and narrative) of the game. A thug isn't just a thug, they're a thug who shrugs off blaster fire: suddenly just pointing a gun at them isn't enough. A bank heist looks increasingly like a special forces raid and is similarly difficult to defeat. Even if guns are hard to come by, making civilians tougher will tend to make them bolder and more confident.
Actually, you can look at this quite mechanically: really good ubiquitous armour arguably makes the hitpoint model make more sense, since you can view it as chipping away at someone's armour until they actually take a hit.
Why does this matter?
This mostly seems like setting material, which matters for Monitors but isn't really relevant to a general discussion of equipment in games. The reason I'm bringing it up is... okay, it's partly sheer completionism. But I do think it affects games in general, because the availability of martial equipment will affect the tone of a game.
A game where everyone carries weaponry tends to have an edge to it. You don't need guns in a techno-utopia where everyone is happy and there's no crime; even if you want sport shooting, there is literally no reason to carry them around. It would just be really inconvenient; nobody walks around with a gas mask for the sheer heck of it.* If you carry guns, there should be a reasonable chance that you need them.** You may need them to defend against external threats, like alien invasion, in which case your society as a whole is threatened. Or you may need them to defend against internal threats, like criminals. Some problems, like armed insurrection or terrorism, combine aspects of both. In any case, these will come across as troubled places where everyone keeps an eye out for danger. You might play that darkly, you might play it for laughs - a game where every pensioner on the street whips out blasters to fend off the Martians is fun too.
Of course, a second possibility is that the population is under an elaborate deception by governments or some other agency, and no real threat exists. Again, hardly the stuff of utopia, and a game in such a setting is likely to have an edge to it.
Another point is that it will affect the relationship between PCs and NPCs. If NPCs are routinely armed, then carrying weapons isn't a distinguishing feature of PCs. You can also probably assume that PCs aren't the only ones willing to intervene when trouble occurs.*** PCs may expect to be confronted by well-meaning or alarmed NPCs, as well as by actual antagonists, and have to identify and handle these situations appropriately (in some genres, killing both). NPCs are less likely to be hapless bystanders; any armed citizen can (and, potentially, should) respond to a crisis. The emotional reaction to NPC behaviour may be different, and the ways they're expected to behave too.
Of course, if PCs are not do-gooders, then they'll be confronted by armed civilians during their crimes, and will have to defeat them; killing innocents generally means a darker tone than simply robbing them.
Consider the Generic Western setting, where Colts and rifles are commonplace. Respect is often won through displays of skill with a gun, and refusal to draw is cowardly - or shows level-headed heroism, or maturity. Unassuming lawyers, doctors or bartenders display heroism by taking up guns in the face of the Brady Gang, often acting as allies or examples to a protagonist. Apparent strong men refuse to fight and show their true nature; weaklings confront villains and are ennobled, even though they often die for it. The protagonist might be the Mysterious Nameless Hero, but they aren't the only one with a gun, and often the way others try and fail to overcome a threat highlights its severity.
Shipboard Space Opera is another potential example. Quite often every crew member carries a gun, and is trained to use it. The protagonists can't distinguish themselves by being the ones who confront a threat facing their civilian protectees. They rely on other traits instead: they may be the commanders responsible for important decisions, they may make political moves, they may possess extraordinary abilities that still distinguish them qualitatively from their comrades, or they may simply outclass them. Even in the latter case, the relationship is not "knight and helpless peasants" or "shepherd and sheep", but "ace and plucky comrades".
* Okay, certain steampunk enthusiasts aside.
** Note, "should"... assume the game reality makes more sense than, say, large swathes of the United States.
*** Obviously, PCs other than classic adventurer tropes are available. If you are playing voices in the mind of a hedgehog coming to grips with the death of its father, or any game where physical confrontation plays a minimal part and PCs don't intervene when trouble occurs, this isn't very relevant.