What are some possible causes for a droopy eyelid that's a bit puffy?

Local problem. It all depends on your clinical evaluation. You may have a cyst in your eyelid or other lesion that makes your eyelid react and become heavier. You need to see an eye doctor to be carefully examined.
Droopy eyelids. Droopy eyelids can be due to excess skin on the lid, too much fatty tissue, weakness of the elevator muscle of the lid or a combination of all these.
Many causes. Drooping of an eyelid can be caused by many factors. Sagging of the brow can make the upper eyelid appear heavy and lax as can the combination of poor skin elasticity and protruding fat. Finally, the muscle that supports the upper eyelid can become weakened, resulting in a tired or droopy appearance of the lid. A specialist in cosmetic surgery can help you understand your situation.