The Crimson Binome
Hero
The penalty is just that you don't get the normal benefit of it being Heavy: that it qualifies for a certain feat which only applies to Heavy weapons. If you make Heavy weapons inherently deal more damage, then every non-small character would choose the heavy version of their normal weapon because it does extra damage and there's no downside for them.Heavy is put as some kind of penalty for playing "small" character.
You need lighter weapon, that means smaller damage.
You have a war-axe and a great-axe, and the only difference is that the great-axe is Heavy and does more damage, so every dwarf ever will choose the great-axe over the war-axe because the great-axe is just better. There's no interesting choice here. You might as well just make a rule that says non-small characters do +1 damage with two-handed weapons.