Hitting for the most part is done on one leg at a time. Consider the stride and the hitter is bracing his/her weight on the back leg. Once the front foot hits, weight is transferred to the front leg - at least it should be. This is dynamic balance.
Either way though, weight should be on the inside of the foot - not on the heel and not on the ball of the foot. This is the best way for the single leg to brace and stabilize against the weight shifts.
I mainly help girls ages 10- 15 and once in a while they fall forward after contact.Problem is, too many people take this "balance" cue and interpret it as you should never be falling over the plate after a swing.