I have a slightly different take than Jasper, about doctors. Most all of them have been taught that TSH is the only test needed to determine a person's thyroid status. This is totally wrong. Due to the number of different steps in the total thyroid process, and the numerous variables involved, TSH has a negligible correlation with hypothyroid symptoms, which are the cause for patient concerns. For the same reasons, the active thyroid hormones Free T4 and Free T3 have only a fair correlation with hypo symptoms. Every person can have different levels of thyroid at which they feel normal. If you will click on my name and then scroll down to my Journal you will find an Overview to a paper: Diagnosing and Treating Hypothyroidism: A Patient's Perspective. In the Overview you will notice Suggestion no. 6;
"Since symptomatic change is strongly associated with serum FT3, and less with FT4 and TSH levels, the current treatment protocol based on L-T4, titrated to just return TSH within range, cannot guarantee that FT4 and FT3 levels are adequate for clinical euthyroidism. Instead, when hypothyroid symptoms persist, the patient’s FT4 and FT3 levels should both be increased enough to relieve signs/symptoms of hypothyroidism without creating signs/symptoms of hyperthyroidism. TSH alone cannot reliably determine that the medication dosage is adequate to restore the euthyroid state."
So you don't have to find an Endo, just a good thyroid doctor that will test for Free T4, Free T3, Vitamin D, B12 and ferritin, and sometimes cortisol and Reverse T3. The doctor must also be willing to treat as described in Sugg. 6.
I should also mention that metabolism is very important to your weight and thyroid is very important to your metabolism. There is information that inadequate thyroid levels can reduce your Resting Metabolic Rate (RMR) by as much as 200 calories per day, up to as much as 900 calories per day in extreme cases. When you look at the formula for estimating RMR for women, it will reveal that if your RMR does down by 200 calories per day, with no other change in diet or exercise, you would gain over some time, about 46 pounds.
If you will tell us your location perhaps someone can suggest a doctor that has been recommended by other thyroid patients.
Most primary care physicians don't understand the nuances of thyroid testing. If you are seeing one, I would recommend seeing an endocrinologist. If you are already seeing an endo then find one that is willing to treat you based on symptoms and not just a number. It takes a bit of searching but they are out there. Your dosage is pretty low and your TSH is more on the hypo range. This is based on the very limited info in your post. Insist on the complete thyroid panel test which includes Free T4, T3 and total T3 to start.