It's my T4 that is elevated, when I was diagnosed my doctor told me it was extreme hyperthyroid.
Just wondering what hormone level you referred to in your post? If your TSH went from 2.5 to 4.7, you are probably hypothyroid, which could be the cause of the weight gain. If you refer to T4 levels, then it would be a different story.
Fun, isn't it? A lot of doctors will insist weight gain has little to do with thyroid. While I guess I see their point, I have a feeling it has more to do with weight gain than they'd admit!
You might want to have your adrenals checked. DHEA and cortisol. Adrenal fatigue has the same symptoms as hypothyroidism and weight gain is one of them.