The most likely thing still is that this is a subtle manifestation of eye allergies, also known as allergic conjunctivitis. As you know of course, most commonly allergic conjunctivitis will have symptoms like a sensation of dryness, as well as redness and itching. Sometimes, however, the only symptoms may be excessive tearing. This is especially true if you already have a history of seasonal or environmental allergies. If so, I would suggest treating this as you normally would (avoiding dust, smoke, and potential allergens; taking an antihistamine medication like Zyrtec (cetirizine) or Claritin (loratidine)) and seeing what happens. If things do not clear up then you might want to go see your doctor
Other potential causes of eye tearing would include an infection with a virus or bacteria (unlikely without more severe symptoms), trouble with dirty contact lenses
(if you wear contacts), a small scrape or scratch on the eye (more likely if the tearing is more in one eye than in the other).
Please discuss this issue with your primary care doctor
. They will be able to make an assessment and determine whether any specific treatment is needed.