Ever taken a good look at the weapon list in 5e D&D? You should. It's a great example of negative design- that is, it's a great example of what you should not do.
Consider the handaxe versus the mace. The handaxe costs 5gp, does 1d6 damage, is light, and can be thrown. It's useful for two-weapon fighters, it does decent damage, and is a ranged weapon in a pinch. You can dual wield a battle-axe and a hand-axe, throw the hand-axe, and then two hand grip the battleaxe for extra damage afterwards. How cool is that?
The mace, on the other hand. It costs 5gp and does 1d6 damage. That's it. Can't throw it, by the rules, and it's of no use to a two-weapon fighter. Hmm.
Another, quicker example: Is there any reason a trident costs 5x as much as a spear despite having identical stats?
Even quicker: why does a scimitar cost 25gp when the literally identical (and on the next space down) shortsword cost the same?
Faster still: Why would anybody ever buy a flail?
I gotta fix this.
Ok, so this is what I came up with. This took me like, an hour that I would have otherwise spent doing nothing at all.
First, I changed up the weapon rules. The light and heavy designations were super arbitrary and just makes it harder for player characters to be larger or smaller than normal without really being much simpler. So now it works like this:
Light: A light weapon is a weapon that is one size smaller than the creature wielding this. When a creature is wielding a light weapon in its offhand when it makes an attack, it may use a bonus action to also attack with that weapon. Don't apply your ability modifiers to the damage of that attack (unless it's negative).
Heavy: A heavy weapon is a weapon that's two sizes larger than the creature wielding it. You have disadvantage on an attack roll with a heavy weapon.
Handedness: You can wield a weapon your size or smaller in one hand. You must wield a weapon one size larger than your own size in two hands.
Versatile changes, too, but only a little:
Versatile: If you wield a versatile weapon in two hands when you would normally be able to wield it in one hand, you may increase the damage die by one step.
This means that if you're a small fighter, you can two-hand a spear but you don't get the bigger dice when you do. Sorry.
So, that was easy. Now all that's left is to give all the weapons sizes. This is also easy: if a weapon was light before, that meant that it could be wielded in an off-hand by anybody. So we make it tiny, one size smaller than small. If it was one-handed, we make it small. If it was heavy, we make it medium. And if it was two-handed only, we make it large. Note that most two-handed weapons were also heavy, which is 5e's explicit 'no shorties' weapon rule.
Since we're talking about weapon sizes, I also wanted to cover the odd case where, let's say, somebody gets a giant's dagger. Or a gnomish greatsword. So I just wrote a quick rule that says:
If you have a weapon that's larger or smaller than the weapons presented here, increase or decrease the damage dice by one step for each size difference.
So without too much fanfare, here's the new chart:
Pretty simple, right? For those without formal weapon training, there's all the basics- daggers, clubs, axes, spears. I gave clubs finesse because I like the idea of eskrima warriors (or whatever) running around. Same with staves. I recognize that makes maces slightly worse than staves, but I don't honestly care. Handaxes, clubs, spears, staves, and maces all do basically the same thing.
Now the weapon list is shorter and it's easier to see what weapons you should be going for. It also reiterates how the weapon list is three times as long as it needs to be- even though 5e has almost completely eliminated typed weapon damage (slashing, bludgeoning, piercing) it still occasionally has creatures that are resistant to one weapon type or another.
If I had my way, either weapons would all do 'weapon damage,' or there would be concrete differences between edged/piercing/blunt weapons a la FantasyCraft. Imagine, swords causing bleed wounds, blunt weapons knocking dudes around, maybe causing stuns, piercing weapons with better crits...
Anyways, this is probably the list I'll be using going forwards. I have ideas about differentiating weapons further, but that's probably design for another game.
Side notes: This is a tiny nerf to small fighters overall- by an average of 1 point per hit. (d6 to d8). I'm not really worried.