All weapons do d6 damage in OD&D. However, some weapons have special abilities, and all weapons have different effects based on how you wield them.
Weapon + shield = +1 AC
Weapon + Weapon = +1 to Hit
Weapon + torch = Visibility, torch can be used as a club, or can set fire to things, but you don’t get the +1 bonus to hit that you’d normally get from dual wielding.
Two-handed Weapon = Roll 2d6 damage, drop the lowest
Ranged Weapon = You’re far away from enemies, that seems like a good enough bonus
Daggers = Anyone can backstab with a dagger, as long as the enemy is surprised or flanked. Backstabbing does double damage. Thieves can backstab with swords or daggers and add their level to the damage roll.
Spears and other weapons with reach = This one is tricky. Right now I’m going with Spears and other long weapons get a free attack on approaching enemies, and additionally can attack from a back rank (behind other PCs). Also, they’re two handed weapons. So they can roll 2d6 and take the highest roll.
Warhammers, maces, and clubs = 2d6 drop the lowest on skeletons and the like. Two-handed warhammers get 2d6 drop the lowest on normal creatures and 3d6 drop the lowest on skeletons, etc. I don’t want to get too into slashing vs. piercing and all of that stuff just yet, so this is kind of a stand-in until I think of something better. They can also be used as fools for pounding in stakes, smashing chests, and wooden doors. And maybe shields don’t get a bonus against. I’m not sure.
The point is basically that I want a way to differentiate weapons in a simple way that’s not just window dressing. Also, I want the weapons PCs choose to be about how they approach combat as a problem, first, flavor second, and then of course damage third or not at all. Since damage is largely flat (besides two handed weapons) you can just play how you want to play.
Maybe this is already a solved problem and variance in damage dice is fun. But for some reason I feel like my players are always choosing whatever weapon they can legally play in their class which does the most damage. Which at that point - I’d rather just make the damage the same and give each weapon a unique property or ability. Like Spears can trip people.
As usual, this is pretty heavily inspired by Philotomy.