I am not a doctor, but I would suggest a second opinion. I have Hashimoto’s (autoimmune thyroiditis — hypo) but my Mom has Graves (hyper). Your doctor may be right, but it can help to get that second opinion.
I also have celiac disease (another autoimmune issue) that is often linked to thyroiditis. You might consider ruling out celiac disease which can contribute to weight loss as does having a hyper thyroid.
You doctor may want to see if your thyroid calms down on its own instead of offering medication. Again, a second opinion can put your mind at ease.
In any case, close monitoring should be done. Graves can impact your bones and affect your eyes. Take care!