How common is it for somebody to get drooping eyelid?

Not common: Drooping lids occur as a congenital defect, an acquired problem from trauma, a nerve problem from disruption of the 3rd cranial nerve, a consequence of muscle disorders and myaesthenia, and related to skin relaxation and fat deposition in the elderly. Many of these can be helped with surgery. Most people do not have such problems so the condition is not common.

Drooping eyelid: This problem is common. Your best bet would be to have your eyes evaluated by a board certified facial plastic surgeon.