Puffy upper eyelids caused by hyperthyroidism usually require regular medication to recover, and how long it takes to go away varies from person to person. Some patients may show improvement after about 3 months on medication, but some patients still have puffy eyelids even after 1 year on medication.
In any case, it is important to control hyperthyroidism to treat the eyelid swelling, and the medication should be administered at the right time and in the right amount, with regular reviews.