If you haven't read Stop the Thyroid Madness book and/or website I highly recommend it. A properly working Thyroid and Adrenal system should help with the weight loss.
Also Iodine by David Brownstein and The Iodine Crisis by Lynn Farrow. I really liked both of those.
Iodine supplementation guide
Are you deficient? - The Iodine Project
The list of things being deficient in Iodine can be a part in is pretty large. I just read those two books and it was very interesting.
tinyurl.com/iodine-references.com is also a great site detailing supplementation of Iodine.
Iodine also helps to balance hormones. I've heard it increases Testosterone and balances estrogen types. Very good stuff. Many people are deficient especially because of the bromide, fluoride, perchlorate's, and other toxins that use the same receptors as Iodine when we are deficient.
Supplementing Iodine along with co-supplements sounds like a very good idea. The estimate I read recently is that it would take about 4 pounds of fish a day to have sufficient Iodine. It would be less probably if you avoid all toxins, but you'd have to avoid everything using Bromide which is a ton of things in today's environment. They use it as a flame retardant in furniture and stuff.