Aghhh! Hypothyroidism---not as fun as it sounds! Here's the thing, I had Graves disease--severely hyperthyroid--my internist performed a radioactive iodine ablation and *BAM* instant hypothyroidism. That was 19 years ago.
While it's true that the medication MAY help you lose weight, your doctor may be hesitant to put you on enough of the medication to ever have a normal metabolism. Do some research online and you'll find a much more medical explanation, but simply put, they are so grateful to see you at anything in the normal range---by this they mean LOW normal---they are done. Some folks never get to anywhere near normal. I'm sure it's frustrating to be losing more slowly, but this is not a condition you really want to deal with the rest of your life.