When can go back to the gym? And when I can start sunbathing?

After an upper blepharoplasty, I tell my patients to take it easy the first week. No heavy lifting or head dependent activities. After a week, they can start to perform light exercise ramping up to full exercise at two weeks. Sun "tanning" is always frowned upon due to skin damage, but a spray tan could be done at any time after the sutures are removed. I would personally wait until all bruising and swelling resolves. Andrew Campbell, M.D.Facial Rejuvenation SpecialistQuintessa Aesthetic Centers

Thank you for your question. The first week you will be very limited. I recommend waiting anywhere from 2-4 weeks for exercise. I would avoid sunbathing to avoid any complications. Best of luck!Dhaval M. Patel Double Board Certified Plastic Surgeon Hoffman Estates Barrington Oakbrook Chicago 

Most likely you need between 2 weeks to a month before the incisions are healed and probably another month for the swelling to fully resolve. Sometimes longer.
I would tell you back to the gym at 1 month and strenuous exercise at 6 weeks.
It will never be a good idea to expose your incisions (or any other area) to the damaging effects of sunlight.