CRGreathouse said:If it's a function of impulse, the weapon itself would be irrelevant - one could impart about the same impulse on a light weapon as a heavy weapon. Unless it's extreme on either end (low impulse for a 1 pound or 100 pound object), it's irrelevant.
Try to tell that to a baseball player, and you'll probably be laughed at.
I'll say again, over-analysis outside of a classroom is apt to be trouble. And despite that, I'll try some more explanations.

To a certain degree, you are, in fact, correct. If you picked up a baseball bat, and used it on a human body, for the most part the actual weight of the bat wouldn't matter much in doing damage that body.
However, if you think energy is a real issue, then with a naive analysis, heavy weapons would be right out. Bastoche notes that you should be able to swing a light weapon faster, and the energy varies more strongly with speed than weight. And, while the gravity assist you mention exists, it isn't very strong - it will never add more energy to the strike than you'd get out of dropping it from that height. How heavy will the weapon need to be before that extra energy would be notable?
In more complete analysis, we find the mechanics of muscles and the human body are a bit daft, and defy common sense (and Bastoche) at times. Especially for very highly muscled individuals, the maximum swing speed is not as dependant on the weapon mass as you might think. The individual becomes limited not by how much the muscles can lift, but by limits on how fast muscles contract. Gregor the Mighty can probably swing a smaller object about as fast as a much heavier one, and so it'd behoove him to use the heavier weapon.
Also, I repeat that the damage done is more related to impulse - change in momentum - than it is on energy. And you see, the momentum the thing has got to impart is equal to it's mass times velocity (p=mv). That means that if I can notably increase the mass with only slight decrease in speed (say, by putting the mass at the end of a long handle), my potential damage can increase.