Please check your lab report again. Neither of those numbers looks like a T3 number or a T4 number. Also, reference ("normal") ranges vary lab to lab, so you have to post those from your lab report as well.
Graves' will often go into remission and can stay in remission for years. Your doctor probably wants to see if yours goes into remission before trying a more permanent solution, like radiation or surgery. Once your thyroid has been removed or destroyed, you will be hypo for the rest of your life, and that comes with its own set of problems.
yes I have graves. my levels were .03 t3 t4 73 not sure what that meant
Please post recent thyroid labs and include reference ranges, which vary lab to lab and have to come from your own lab report. Weight gain can be a symptom of hypothyroidism (overmedication for hypethyroidism). Do you have other hypo symptoms? It could be that you just need a slight reduction in meds.
"...I want to do the radiation and be done..."
You do understand that once your thyroid has been destroyed by radiation, you will be hypo and dependent on replacement thyroid hormones for the rest of your life? You will never be "done" with this if your thyroid is irradiated.
Have you been diagnosed with Graves'?