Tearing eyes can be classified into two possible reasons: 1) ocular irritation causing reflexive tearing or 2) a blocked tear drainage duct causing an overflow of natural tears.
Tearing that is intermittent is most likely due to ocular irritation from dryness, allergies, or irritants in the air.  Treatments include managing dry eyes or removing the allergen or irritant.
Tearing from a blocked tear duct is much less common.  This tearing is present all waking hours without relief and typically does not fluctuate depending on activity, environment, or dry eye therapy.  It can be confirmed and usually treated in the clinic.