You have to eat an awful lot of calories to gain 16 pounds in a month!! Unless you are really fooling yourself about how much you are eating, this really sounds like something medical. If your endo isn't listening, you may need to find another. You should also ask about having cortisol levels checked... I've hear about cortisol issues causing extreme rapid weight gain.

Also, I would recommend that you not take the generic thyroid medication. Ask your doctor for Synthroid or one of the natural thyroid replacements. I don't think those generics work right.

I have hypothyroidism and although my levels are stable due to constant monitoring and medication corrections, I gain weight very easily and have to diligently watch my diet. If I don't eat enough, I will sometimes gain weight. If I exercise too hard and don't properly fuel myself I will gain weight. So, I have to balance the exercise with a healthy 1500-1600 calories a day. If I go too much below or too much above that, I gain weight.

Also, not sure of your age -- but weight gain gets worse during peri-menopause and beyond. I found it was much worse during peri-menopause than it is now that I am post-menopause.