A watery eye may actually be a dry eye due to poor tear film constitution resulting in reflex watering due to irritation of the ocular surface. (See Dry Eye for details)
Occasionally, the nasolacrimal duct may be blocked. This is the passage whereby tears flow from the eyelids to the nose.
A simple, pain free, test called a sac washout can be done to find out if you have a blockage.
Unfortunately the only treatment is surgery.