I've gained weight since turning 40. It's as if my metabolism completely shut down. I'm on the pill for ovarian cysts, can this be the culprit?

Definitly not. Ovarian cysts do not cause weight gain or slowing of the metabolism. Perhaps you are thinking of polycystic ovarian syndrome where weight gain and slow metabolism cause the ovary to exhibit typical finding of multiple small 1 cm cysts. These cysts are a result not the cause.