Hi, I too have an underactive thyroid. I gained about almost 50 lbs after being diagnosed. While I take medication, I still think our bodies don't work the same as people without endorcine issues--the whole "just cut your calories and workout" theroy just doesn't cut it---or for me it didn't.
I have been working out and reducing my carbs (replacing refined carbs with vegetables or keeping net carbs to 100-150g daily), the weight SLOWLY started to come off. Then recently I read that the fat hormone leptin is often the primary cause of many of the hypothyroid symptoms in overweight individuals so just recently, I started to follow the "leptin diet" rules:
Rule 1: Never eat after dinner.
Rule 2: Eat three meals a day (do not snack).*
Rule 3: Do not eat large meals.
Rule 4: Eat a breakfast containing protein.
Rule 5: Reduce the amount of carbohydrates eaten.
*should stay full for 3-4 hours between meals or you are not eating enough or not the right foods, feeling full beyond 4-5 hours means you've eaten too much http://wellnessmama.com/5356/cravings-fix-your-leptin/
In addition to the 5 rules, I'd also add getting a good nights sleep. There is some recommended nutrients that are important for proper thyroid function (if you google, you'll find lots of information). If you don't think you can get proper nutriets from whole foods, then consider supplements.
Hope that helps! Everyone is different so try different things and see what your body responds to.