Why do the eyes water all the time; would it be infection or allergies?

Most common-allergy: Eye allergens are common to cause daily itching, dryness and irritation along with watering... Watery eyes may also be due to "chronic dry eyes".

Reflex tearing : Reflex tearing occurs when the eyes get irritated and dry, your description sounds like dry eye. Initial treatment is frequent artificial tears during the day, ountment at night, warm compresses a few times a day, and omega-3 fatty acid supplements. If no improvement, you should see an eye doctor for further evaluation.