Heavier BBs maintian their inertia better, they hit harder and at longer ranges, and are more accurate at longer ranges too. One thing I've separated when explaining to people about maximum range, is this: Are you referring to the maximum distance you can hit something, or the maximum range where the BB lands? Due to air, a lighter BB will travel farther before it comes ot rest than a heavier one, but a heavier one will travel farther more accurately.
And to rehash, heavier BBs DO hit harder. Try a 0.20g fired out of a GBB at 100ft, and a 0.43g BB out of the same gun, next shot at 100ft. You WILL feel the hit (and leave a lump if it hits you on the top of the head, right Chef/Jackals?) a lot more with the heavier BB. If you don't feel like having or being a human target, shoot at something hard yet hollow about 100-140ft away, like a plywood wall of a shed. A lighter BB will give you a tick sound, a heavier one will give you a loud THWACK!!!