Watery eyes can be due to many factors and conditions.
In infants, persistent watery eyes are commonly the result of blocked tear ducts. The tear ducts carry away tears, like a drain, and if they become blocked the tears overflow onto the face.
Stagnant tears in the tear ducts increase the risk of infection, and the eye will produce a sticky liquid, making the problem worse. Infection can also lead to inflammation on the side of the nose, next to the eye.