Hi there. While I have never used the provera, it is a progestin, and it seems that progestins (progesterones) put weight on almost all women. I am not sure of the actual mechanics of it, but it is almost a universal side effect of progesterone, particularly if it is out of balance with estrogen, which it would be if it is preventing menstration.
I belong to a menopause website which deals quite intricately with hormone replacement of all types, and there are members there as young as their 20s and as old as their 60s.
If you feel good on the provera, and don't want to quit I would suggest you track your diet really well. I think the reason the P packs on the pounds is twofold. Number one it seriously increases your appetite, it is like being in that PMS week where you have the ravenous appetite all the time!! Number two, it has a calming effect on most people and it possibly slows down your metabolism, so even if you don't change what you eat, you will still gain weight. In order for you to MAINTAIN your weight, your only answer is to cut your calories and increase your activity. Also make sure you are drinking lots of water, as P can also cause fluid retention (again, think of that PMS week). You CAN lose weight on the P, but you will probably have to try a little bit harder than if you weren't taking it.
I wish you good luck!!