This is an old thread, but folks need to know why any thyroid hormone production, via T4 or iodine can cause weight gain.
T3 is our metabolism and temperature hormone.
ReverseT3 (RT3) is what stops T3.
T4 converts to both T3 and RT3.
When RT3 rises, it is due to things like inflammation, illness, diseases,low calorie dieting a month or more, selenium and other nutrient deficiencies, thyroid damage, etc and we get fat and cold.
Stopping the inflammation, raising our immune system (D3) and d-selenomethionine help, but stubborn cases may need to take T3 in order to flush out the RT3 to reset it.
With Hashi's one needs to be on thyroid hormone to bring the TSH below 1 for 6-8 weeks while on D3 and selenium in order to stop the thyroid peroxidase antibody attack on the thyroid. After TPO-ab lowers to normal, they can reduce thyroid hormone and introduce iodine until normal thyroid hormone production improves. If thyroid damage excessive, they may have to be on thyroid hormones for life.
Please see Dr Alex Haskel's videos for Hashimoto's for more info.