What categories of weapons do we "need" to make the weapon choices distinct, mechanically, even if it -in meta-game terms- is a minute difference?
I tend to work with:
- Weight: Light and Heavy. You really don't need a "medium" because if something isn't light and it isn't heavy, then it's just "normal." Differences: Light weapons -by definition- may be used one to each hand for "dual-wielding"f fighting styles. Heavy weapons require two-hands, hence automatically "no shield" and -if you want a more minutia mechanical difference- go last (or at least receive some kind of penalty) on initiative in exchange for higher damage.
- Hands: Versatile and Two-handed: If it's not "able to be used with two-hands sometimes" [for increased damage] or "needs to be two-handed all of the time," then obviously, it's single handed. Differences: self explanatory.
- Type: Missile [or "Ranged"] and Melee [my version of "Martial" weapons]. kinda self-explanatory. If it's not able firing missiles or used predominantly by throwing, it's not a missile weapon. Melee weapons are the big clunky things you need special training or experience to use properly in hand-to-hand combat. If it's not a Missile or Melee weapon then it's obviously a "simple" [per 5e parlance] or "peasant" weapon that just about anyone could pick up and use effectively.
- Damage: Blunt [or "bludgeoning" if you prefer], Slashing, Piercing: and potentially combinations thereof, depending on the weapon, either "half & half" -as a morningstar dealing damage that is bludgeoning and piercing at the same time- or an option for the player for the type of damage they'd like to inflict -as a spear or halberd might be used to pierce or slash. Fairly self-explanatory stuff.
Then there are a few descriptors that might be tacked on to any combination of the above:
- Thrown: the weapon is light or balanced enough that it can be thrown effective enough to deal damage. Some things, like a javelin, is automatically thrown in its normal use, but a hammer or dagger doesn't have to be.
- Reach: a hand-held weapon that can strike someone more than your immediate neighbor. Usually I just bump it to 10 feet, almost always with a two-hands necessary. Those that like to get into the nitties and gritties of historical pole-arms might find/have different/farther reaches. This is not to say an enemy must be that far away to hit them, only that -if they wish- the PC can effectively hit/potentially damage someone at that extended "reach." For ease of play, I tend to just use 10' across the board...unless it's a pike, I guess.

- *Special: kinda lazy [on my part] catchall for anything a weapon can do that's not damage. Nets or whips can or may *entangle, for example. Perhaps a large battle axe or two-handed sword provides an AC bonus from "cover," etc...
I think that suitably covers everything (unless there's something obvious I'm just missing/forgetting at the moment) without being unnecessarily complicated or arcanely obscure.
What do people think? What other categorical terms do you use or prefer or just plain want in the game for more mechanical distinctions?