Many MH meds do make you put on weight. I've been on a bewildering array for a number of years and met others on different MH drugs and discussed this very thing.
OK: not everyone is affected, and some drugs more so than others, but anything that is basically sedative is likely to slow down your systems inside. A very small number of drugs make you feel hungry. Not general anti-depressants, btw, more serious psychiatric meds.
Its cost benefit time: many of us have no choice.
My personal path initially was to carry on exercising a lot as I always did, but cannot do this much now. Reasonably vigorous exercise as it were makes the digestion work better as well as calorie loss.
So now I practice a very strict diet indeed and I have managed to maintain my weight. It's not a miserable path, I've a far greater appreciation of the foods I do eat and never have fatty or sweet food except on exceptional occasions.
Sorry not to have magic answers!