The majority of people with Graves’ lose weight in the hyper phase. A smaller percentage gain weight. The reason for weight gain is the body goes into survival mode when we are hyper. The body gets tricked into thinking it is on a starvation diet for some folks so the body packs on as much fat as it can from what you eat to help carry the body through what it thinks is lean times.
That being said, once your levels get back to normal, you follow a regular diet, the body realizes it does not need to horde fat and weight loss will slowly begin to happen. It does not happen overnight. Weight loss after gaining in this case is slow but it will happen.
I do not know why some bodies hord while others do not. But give it time.