First thing to understand is that TSH is a pituitary hormone that is affected by so many things that except at extreme levels it is totally inadequate as a diagnostic for thyroid status even in the untreated state. When already taking adequate thyroid medication, the TSH usually becomes suppressed below the range. That doesn't mean hyperthyroidism, unless there are accompanying hyper symptoms due to excessive levels of the biologically active thyroid hormones Free T4 and Free T3. Your Free T4 level is unnecessarily high and apparently you were not tested for Free T3, which is very important. I say that because hypothyroidism is properly defined as "insufficient T3 effect in tissue throughout the body, due to inadequate supply of, or response to, thyroid hormone. So it is the level of Tissue T3 Effect which determines a person's thyroid status, and whether there are symptoms or not. Thyroid medication dosage should never be based on TSH level. Dosage should be adjusted as needed to relieve symptoms.
So a couple of things we need before further discussion. First tell us about any symptoms you have besides weight gain. Next, please confirm that the dose reduction was done based on those tests results. Also, what was the reference range shown on the lab report for the Free T4 result? Since a person's thyroid status is the result of both supply of, and also the response to thyroid hormones at the tissue level, it is important to test for Vitamin D, B12 and ferritin. Has that been done for you? Also have you been tested for cortisol? When you were originally diagnosed and started on thyroid med, what was your TSH level at that time and were you tested for the possibility of autoimmune antibodies associated with Hashi's?