I do have rapid heart beat, between 110-125 because of graves' disease, are there any exercises i can do to lose weight?

Appetite: It's a common misconception to believe that because of the increased metabolism of grave's disease, people will be thin. The fact is most are overweight because graves stimulates the appetite. Advice: get the grave's controlled, then work on reducing your caloric intake. Any form of exercise will help (do something fun!) but won't correct the weight without limiting calories.