It can cause either weight gain or weight loss though I do not personally know what the parameters are to trigger either end of the spectrum. My mother took them but her weight didn't change at all, my aunt who also took them gained a stone during the process, both of which had similar activity levels. I assume you are dieting and not a whole lot of rigorous exercise as you told me it's difficult for you before (osteoporosis I think it was). If weight gain did occur it shouldn't be potent enough to set you back, it would most likely just slow your diet progress assuming you continue with it. While the side-effects are attributed to women over 40 they are just as applicable to you. It's not the age that matters, it's the menopause cycle itself and that age bracket is just a simpler guideline for the majority.
With that said, the doctors would have likely needed information from their superiors because POF is as far as I know a specialty subject. They would most certainly be able to advise you on the side effects of Ellest Duet Conti though it would have been neglectful of them to simply give you the drugs without consulting someone better informed.
I can't really say what I'd do in your position, on the one hand your weight may not change at all and on the other it could, be it increase or decrease. It just depends whether or not it's worth the risk to you, at least until you can find somebody who can tell you for certain or at least give you clarity.