The plastic surgery procedure to remove upper eyelid fat and loose skin or hooding of the eyelids is called an upper blepharoplasty.
The upper blepharoplasty can be done with a scalpel although a modern approach uses the laser blepharoplasty to remove upper eyelid aft and loose skin.
The operation is fairly simple and straight forward if done by an experienced board certified plastic surgeon. Recovery is not painful and usually consists of time for swelling and bruising to go away. Typically, after laser upper blepharoplasty swelling and bruising are gone in 10 days to two weeks at most.
See an upper and lower laser blepharoplasty example.