It stands to reason that all else being equal, a heavier bat swung *at the same speed* will hit the ball harder. The bat has more momentum with more weight, so it recoils less when it hits the ball, and more momentum is imparted to the ball. Also, a heavier bat that is the same size (and made of the same material, i.e. Both wood bats) will also be more dense, and therefore probably less flexible. The less the bat deforms on impact, the more energy is transferred to the ball. This is one reason aluminum bats hit harder than wood bats - they are much stiffer.
Also, the same batter can swing a lighter bat at higher speed than a heavy bat. Aluminum hits hard because it's stiffer and because it can be swung much faster due to its lighter weight.
Really, it's a matter of finding a bat weight that works for the hitter.