Hi Sammycat,
I was diagnosed with Graves back in 1995. I was put on medication, Tapazole and a beta blocker for almost 2 years. I ended up having the radioactive iodine ablation since my liver enzyme levels were going bonkers. I never lost a dramatic amount of weight as I was in the 1% of the people with Graves that actually gained weight to begin with. Once I did the ablation, I went on Synthroid and the weight melted off of me. I felt great for about 5 years. When I was originally diagnosed with Graves, I also had a nodule on my thyroid that I had assumed would shrink along with my gland once I did the ablation. Well the nodule continued to grow and I was diagnosed with Thyroid Cancer in 2000. It has been 11 years now and I feel good. Still battle with the imbalance of the hormones. My weight has crept up over the past few years, mainly due to middle age and my love of wine!
I think you should try the medication first and if that doesn't work then do the ablation. The worst part about the ablation is you have to be isolated from your family for up to 3 days. You may gain some of the weight back since your body probably lost more than it needed to before you were diagnosed. Just maintain a healthy lifestyle and you should be fine.
Good Luck and keep us posted