I, too, have hypothyroidism caused by Hashimoto's Thyroiditis. Typically, if your thyroid hormone dosage is properly adjusted, losing weight is much easier, though some of us still have to work very hard at it. I was diagnosed 7.5 yrs ago and have been struggling with my weight ever since.
Many doctors think that adjusting levels to be just within the reference ranges is good enough and that couldn't be further from the truth... Many of them also adjust thyroid hormone medications based only on the TSH test, without bothering to test the actual hormone levels. You might want to check out the thyroid forum, here on MH for more information on testing/treatment of hypothyroidism... You can access the forum via the following link: http://www.medhelp.org/forums/Thyroid-Disorders/show/73
I'd also like to add that I've lost 25 lbs this year by adding "more" fat to my diet, not less... I went back to full fat dairy, and I use butter, coconut and olive oils to cook with, plus I'm quite liberal with things like avocados, nuts, etc. This doesn't mean a "very" high fat diet, but very low fat, often leaves one feeling hungry, as it did me, whereas adding fat to each meal, is more satisfying, so I actually end up eating less in the long run and I don't get hungry as quickly. Added bonus is that my cholesterol levels have come back into the normal levels and my triglycerides are almost back to normal.
It's also recommended that you do some weight bearing exercises daily, since weight bearing exercises help build muscle and muscle burns more fat.