The reason for a heavier bowling ball is rather simple. Momentum and impulse.
Momentum is defined as mass times velocity (SI unit: KGm/s). Impulse is defined as momentum divided by the contact time (SI unit: N). There are two ways to increase momentum. Either increase the velocity, or increase the mass. The greater the momentum, the greater the impulse (which is basically the force that knocks the pins down). Ideally increasing velocity is better, as in addition to increasing the momentum, it also decreases the contact time. This is also why halving the mass of a bullet quadruples its energy (assuming the same force is applied to launch it--equation for Kinetic Energy is .5mv^2). From this argument, it sounds as if you should simply use as light a bowling ball as possible, since you'll increase momentum more in that fashion. However, there is a definite limit to how fast you can make a bowling ball travel. Your arm simply cannot move that quickly. As such, you should increase the mass of the bowling ball until you reach the point where it starts to compromise the velocity of the bowling ball. Another factor to consider is accuracy. At high velocities, some people cannot accurately roll the bowling ball. Increasing the mass is then an excellent way to still have a considerable momentum while being able to maintain accuracy. I hope this makes sense for everyone.