Along with the excellent suggestions gimel has given, I'd also be curious about your cholesterol, triglyceride and blood glucose levels? My thyroid levels were very similar to yours and it was discovered that I have a condition called Metabolic Syndrome, which is a cluster of conditions consisting of high blood pressure, high blood glucose (fasting blood glucose over 100 is impaired), high triglycerides or cholesterol, excess body fat around the waist. Having just one of the components doesn't qualify as Metabolic Syndrome; you must have at least 3 of them.
Metabolic Syndrome is closely linked to insulin resistance in which the cells in our body don't respond, adequately, to insulin and sugar doesn't enter the cells properly. Instead, insulin shuttles excess blood glucose into fat cells to be stored for later use. Insulin is often called the "fat storage hormone".
With those labs I am surprised your metabolism doesn't seem to be adequate. So, there may be other issues that need to be evaluated. I suggest that you should test for Reverse T3, and Free T3 again so they are from the same blood draw. Also, don't take your thyroid med until after the blood draw, to make sure you don't get false high results. I also suggest that you test for Vitamin D, B12, ferritin, and morning serum cortisol.
The ratio of Free T3 to Reverse T3 is important. High Reverse T3 can negate the effect of your Free T3 level. D should be about 50, B12 in the upper end of its range, and ferritin should be about 70. I am especially curious about your ferritin and cortisol levels because improper levels of is reported to cause pooling of T3 in the blood instead of getting into cells. If you can get those tested, then post them here, along with reference ranges and we will help interpret and advise further.