4loveofthegame,
I suggest you stay with about the same weight bat as you use in a game situation. Most players change to wood for BP and drills which tend to be a little heavier than the aluminum whick is OK. A significantly heavier bat will change your timing. A few dry swings with a weighted bat are good to stimulate your muscles prior to BP. Surprisingly, a very light bat (broomstick) used for hitting soft tossed whiffle balls is an effective training aid in increasing batspeed. As I understand it, the broomstick allows increased batspeed and targets and develops additional muscles. A good hitting instructor is important in developing hitters and should be able to provide you with proper bat weights.
Best of luck,
Fungo