Drooping eyelids. The treatment of a drooping eyelid depends on its cause. If the drooping is due to the stretching or looseness of the eyelid lifting muscle, either a levator advancement procedure (with an incision on the outside) or a mueller muscle/conjunctival resection (incision on the inside of the lid) may be performed under local anesthesia. Congenital drooping may be corrected with a frontalis sling.
Droopy eyelid. There are several causes of a droopy eyelid. Your best bet would be to have your eyes evaluated by a board certified facial plastic surgeon.
With surgery. Droopy eyelid can mean either excess skin hanging over the upper eyelid (dermatochalasis) and/or sagging of the upper eyelid edge (blepharoptosis). Dermatochalsis is corrected with blepharoplasty, where the excess skin is excised. The scar hides well in the upper lid crease. Blepharoptosis is corrected by tighening the muscle that lifts the lid. This is done via lid crease or conjunctival incision.
It depends. Eyelids can be droopy for lots of reasons. In kids it is generally due to a poorly developed muscle. In adults it can be due to a stretched out muscle attachment or due to a disease that affects the muscle's contraction. It is generally fixed by a surgery to either reattach or shorten the muscle and tendon that raise the eyelid, or by using a sling material to suspend the eyelid open.