Well, get ready to put on some more weight, I'm afraid. This, from my experience and talking to others, is a frequent occurance. Trouble is, I haven't found a doc yet who doesn't say "It's not the medication putting on the weight," but when your habits haven't changed and you've been tested, as I have, for cortisol, glucose and other issues, there really isn't anything else it can be. There will be a point when the gain stops, but for me that was about 20 pounds. It took about three weeks to lose about three pounds. Some think that it's because the T4 suppresses the T3, which is what controls your metabolism. I thought that once my levels were normal, the slight weight gains I had due to Hashimoto's would stop but it increased as a side effect of the medication. I can say that exercise and watching your sugar intake has helped me. It's a huge bummer, trying to lose weight that you've gained due to no error on your part, but that seems to be how it is. You may want to talk to a nutritionist about finding guidance on that, but many have no idea about thyroid disorders, so you'll want to lean toward the low-sugar, diabetic-type of eating plans. Good luck and be healthy.
"It's not the medication putting on the weight," TRUE but you may not be getting enough medication - especially when your TSH is over 100 it is indicating that your body is not getting enough thyroid hormone. Thyroid hormone helps regulate metabolism;- without enough of it your metabolism slows which includes how quickly you can burn up your usual fuel stores (but your body doesn't stop storing excess fuel as fat) so it usually leads to weight gain over prolonged periods of time. But you can do things to help slow this progression just as Garnet has pointed out.
I'm sorry Garnet to take issue with your post but I don't agree with the following point;
"Some think that it's because the T4 suppresses the T3, which is what controls your metabolism."
Both thyroid hormones may contribute to metabolism! T3 is faster acting and T4 is slower acting.
T4 does not supress T3!!!! 80% of the total T3 levels actually come directly from T4 conversion in your kidneys and liver. This process is called de-ionation - put simply 1 iodine molecule is broken down/removed from the T4 hormone which results in T3.
The advice about exercise, seeking help from a nutritionist and diabetic-type diets (including low GI diets) is all great advice.
Best wishes and wellness to you both.