Hello,
Let's have a glance at Hypothyroidism. When your thyroid gland doesn't produce thyroid hormone in enough amount, that time we say its a Hypothyroidism. Function of thyroid hormone is to support cell and tissue metabolism in body and generate adequate amount of ATP and convert it into Heat.
In Hypothyroidism due to inadequate level of Thyroid hormone, body metabolism process slow down and patience starts suffering by Fatigue, Heat Intolerance, Weakness, Loss of appetite. Due to Fatigue Weakness and loss of appetite, person tends to avoid physical exercises and starts increase in body weight due to excess fat deposition.
In your case treating physician reducing dose of your medication because your thyroid hormone level becoming normal and your weight gaining might be related to your inadequate physical exercise. You should consult your treating physician so he may review the treatment and possible causes of weight gain. He might suggest you some physical exercises and supportive treatment.

Thanks & Take Care,
Dr. Suraj D.