RECOIL!!!! The lighter bat when hit by a speeding softball, will recoil. A heavier bat continues on it way.
There's no one bat that fits all kids - nor will a bat that's a great fit at the beginning of the season be the right one at the end of the season. Going too heavy not only slows the bat speed down - robbing energy from a potential hit, but it will induce bad swing mechanics as the child attempts to copmpensate for not being strong enough to physically swing the bat. In our game, the other factor is ensuring there's enough batspeed through the strike zone to make contact with a fast moving pitch - faster initial swing should allow for a little more leeway in swing timing (provided the child is capable of adjusting once the swing is started).
And yes, there is a point where having too light a bat isnt helping either - a child able to literally swing themselves out of their shoes should probably move up a notch or two in weight.
I'll spare everyone another lengthy lesson in quantum physics; I never really liked it much myself anyway (Einstein's equation for energy actually refers the energy released by matter as it undergoes fission - suffice it to say this equation is not relative (in any way) in our current context). The equation that is relevant here, is for kinetic energy where energy imparted is equal to 1/2MV2 (1/2 the mass times the velocity squared) - velocity is not a constant and is a *much* more significant contributor to energy than the mass.
A guy named Einstein had a theory that energy was mass squared times velocity. Granted in his theory velocity was the speed of light but it works for softball.
I have read this before and find it to be a very interesting. They also look at the ball and bat at contact.You want to swing a bat with the largest MOI that does not degrade your swing speed and mechanics. Here's a link to an article that explains various aspects of bats and the physics behind it.
Swing Weight: Why moment-of-inertia matters more than weight