If you allow +2 and +3 bonuses at very high ability scores, even a 1 1/2 x multiplier can double the damage a weapon puts out. That's a real advantage for high strength characters, and having lucky 18 STR high rollers running around doing twice the damage of a mere mortal on every hit might get in the way of the character-lightness of the game.
A tamer alternative might be to allow a flat higher rate of damage and say the +2 and +3 bonuses can only be fully obtained using a fully swung two-handed weapon. But by the same token so are the -2 and -3 penalties. (It makes sense, too, to say that small weapons, dagger for sure, and maybe others, have no strength bonus or penalty whatsoever.)
Two-handed weapons need some love because they are going to suffer from a no-shield drawback, plus the other drawback my formation-conscious house rules require: they need a wide swing frontage to use, 7 feet of space at least.
Combine with the basic sword, axe and mace principles and we get this:
All two-handed weapons:
- cannot be used with a shield;
- apply the full +/-2 and +/-3 strength modifiers to damage , while normal sized weapons have a maximum damage modifier of +/-1 (to hit modifiers are the same);
- take up 7' of swing frontage, so only fit in a 10' corridor with someone else who is using a 3' weapon (spear, dagger, shortsword, longsword used as a shortsword).
Two-handed axes do 1d10 damage, and punch through armor in the same manner as one-handed; +1 to hit for every 3 points of physical armor on the target.
Two handed maces and hammers do a base 1d8+1 damage, and have the same armor-class to hit bonuses as the one-handed variety; if a flanged mace or a hammer, the same as an axe; if a spiked mace, +1 damage vs. opponents with 2 points of armor or fewer.