There are several causes for watery eyes: allergies, blocked naso-tear duct,and infection in tear sac are the most common. Some causes that are not as common include: a blockage in the little opening leading to the naso-tear duct, drooping of the lower lid, polyps inside the nose, some sort of irritation such as ingrown eyelashes or a small piece of grit lodged under an eyelid although with both your eyes watering some of these less common causes don't seem applicable.
I would recommend you see an ophthamologist soon and have a complete eye exam. An eye doctor will be able to tell you right away what is going on.
Please let me know if I can be of further help to you.