What can cause my boyfriends eyes to keep tearing, and what steps can I take to revent from going to doctors?

Tearing. The answer depends on age and whether it is one or both eyes. If only one eye it may be a blockage in the tear drainage system or small abnormality in the eyelid position. If both then anything that causes ocular irritation such as allergy, eyelid inflammation (blepharitis), or even dry eye. Dry eye can cause tearing because the quality of the tear film is poor and the eye makes excess liquid tears.
Dry eye. There are a lot of causes for tearing. The number one cause of tearing is actually dry eye. He can try doing warm compresses with a wash cloth soaked in warm water, as well as over the counter lubricating drops a few times a day. If that does not help his symptoms then he should see an opthalmologist to rule out other causes of tearing.
Simple steps. Chronic tearing of both eyes is most commonly "dry eye" or allergy. If he wears contact lenses, take them out, see how he does. Try a commercial artificial tear 1 drop each eye 3-4 times a day. Apply a warm compress every morning. Allergy and infections often have itching and redness. If his tear drainage system is blocked, only doc can fix. If the above steps do not help, best to see a doctor.