I recently started on some new Birth Control (Depo-Provera), and a major side effect is weight gain. It's pretty much guaranteed.
I ALWAYS feel hungry now, and I stopped losing weight entirely. I've managed to keep from gaining, for now, but I don't know how long that will last at this rate.

Has anyone else had (or are having) this experience? Any advice?

Any reason why you want to be on birth control that makes you hungry all the time? Ocella actually makes me feel better, not worse, so if you have a choice I recommend it.

You may want to look at this similar topic: Can Birth Control Slow My Weight Loss

Gaining on Depo is far from guaranteed. I actually lose better while on depo then when not because it gets rid of my cravings except for the week-ish prior to a new shot being due.

that said your body is not my body and is likely reacting differently. any hormone you put into your body can have the effect of altering your cravings. When i am on the pill, for example, i crave bacon cheeseburgers and brownies CONSTANTLY which hinders my loss as my control gets shaky when the craving persist for long periods of time.

If you are finding that you are constantly battling cravings while on Depo then the best bet is to find a different birth control, why torture yourself.