Well if she won't test for for Free T3, and only pays attention to TSH, it is unlikely that she will consider that she is wrong. You could try by giving her a copy of the entire link I gave you above. Or you can try to find a good thyroid doctor elsewhere. If you will tell us where you are located in Iowa perhaps we can come up with a better option for you.
I am at work now and will look up my results. And my dr will test for free t4 but will never test for free t3. I have yet to find a dr in iowa that does. She changed my dosage because of the jump in tsh. That is her baby. Iowa has no thyroid specialists that I am aware of. I think she is a diabetic dr who was told "here have the thyroid patients too". But she is an endocrinologist and as I am seeing her,other drs won't discuss thyroid with me.I have been thru the mill with drs and thyroid issues. It takes 6 mos to get a yearly appointment.
Lots to talk about here. After a TT, you are totally dependent on thyroid medication. You are taking a T4 med, now at a dosage of 200 per day, plus an extra dose on Sunday. So the first question is whether you have been tested beyond TSH, for the biologically active thyroid hormones, Free T4 and Free T3 (not the same as Total T4 and Total T3)? If so, please post results and reference ranges shown on the lab report.
Even more important, what symptoms do you have other than the weight gain you mentioned?
After a weight gain doctors like to keep TSH suppressed. Is that what your doctor was doing? If your TSH is not suppressed by 200 mcg of T4, then it is likely that you need some T3 in your med. Not only that, but Free T3 is the thyroid hormone metabolized by all the cells of your body. Free T3 typically should be in the upper half of its range, and adjusted from there as needed to relieve hypo symptoms. Along with that Free T4 should be at least mid-range. In addition, hypo patients are frequently deficient in Vitamin D, B12 and ferritin. If not tested for those you need to do so and then supplement as needed to optimize. D should be at least 50 ng/mL, B12 in the upper end of its range, and ferritin should be at least 100. You can read about all this in the following link.
http://www.thyroiduk.org.uk/tuk/TUK_PDFs/diagnosis_and_treatment_of_hypothyroidism_issue_1.pdf
A good thyroid doctor will treat a hypothyroid patient clinically by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms, without being influenced by resultant TSH levels. Symptom relief should be all important, not just test results. You need a good thyroid doctor and I am not convinced at this point that you have one and are getting the kind of treatment you need.
Hypothyroidism is not the only cause for diabetes, however, inadequate treatment of hypothyroidism, longer term, can lead to diabetes.