Hi guys, I'm also hypothyroid and I struggled for a long time with losing weight. I'm now enjoying nearly a 1 lb loss a week. I'll just pass along what I did, you could give it a try and see if it works for you.
First, it is all about consuming less food than your activity (calorie deficit). Supposedly a deficit of 3,500 in a week will equal 1 lb of loss. Some people eat the same stuff but just less to achieve this. I have found that food choices allow you to reduce you calories without eating less. So many packaged foods that aren't very filling are packed with calories. Exchanging high-calorie, low nutrient foods for good proteins, fresh fruits and veggies is the easiest way.
And while lower calories help, I think our bodies (or at least mine) was all screwed up from a metabolism standpoint. I saw this Dr. Oz show (not a fan but the guest on this show was hypothroid, worked out like mad, lost nothing). She believes we can balance our hormones through food and it's very easy. In January, I started doing her suggestions. Prior to this I pretty much snacked all day and exercised and only saw a 2 lb loss in 1 year! Pathetic. http://www.doctoroz.com/episode/melt-fat-fast-how-reset-your-secret-fat-loss-hormones?video=15580
If you are leary about links, just good "Melt Fat Fast: How to Reset Your Secret Fat-Loss Hormones".
But I stopped working out and as she suggested, reset my body with daily cinnamon, upping my omega 3 fats, not eating between meals, not eating 3-4 hours before bed, etc., Then reintroduced working out once I felt my body was ready. It could be all coincidence but I figure it's worth passing along as it may help someone else.