State requirement is the most important. Here in MD it's 30 lbs. for deer and bear. More important than draw weight, however, is kinetic energy, meaning you can get away with a lighter draw weight assuming you have a heavier arrow/broadhead combo. Remember your physics from high school? F=mv.
Velocity (v) is a function of a few things. Assuming all bows are equal, which they aren't of course, the three things that would affect "v" would be your string acceleration, string force (draw weight, basically), and draw length. The only way to really affect acceleration is to buy a new bow, so we can count that out. Draw length is going to be pretty much constant, so changing your draw weight is the only variable factor, but it only has a fraction of an effect, and that fraction is only on a fraction of the equation. Therefore the effect is minimal.
BUT, heavier arrows ("m") have a direct effect on part of the equation, so shooting heavier arrows is a better way to increase penetration. That and quality, DEPENDABLE (no o ring to fail), heavy broadheads will be more effective on larger game.
To avoid arguments, I'm not talking about animals jumping the string, only penetration. Also, I'm not advocating using a 30lbs draw weight on Alaskan moose, just saying that going from 60-70 lbs will not be as effective as shooting arrows that are 50 gr heavier.