Dogs may have some watery eyes for several reasons:
1. Allergies. Dogs who have allergy issues often get a brownish discharge under their eyes from the eyes constantly running. We call this 'tear staining' and it usually goes away once they have the allergies under control through the use of medications such as Temaril P or Atopica, both of which are made specificially for allergy issues.
2. Eye injuries. Dogs who have scratched their eyes either through play or through some kind of trauma (like running through the woods) can have eyes that water. Usually it's only on the side where the injury has occurred and will clear up once the eye is treated with medication and healed.
3. Infection. Dogs with eye infections can have weepy eyes. Sometimes the discharge is greenish or even yellow and usually clears up once the dog has been placed on an antibiotic and gotten the infection cleared up.
Regardless of the reason, if your dog's eyes didn't weep before and they're doing it now, it's a wise choice to have the vet take a peek, just to be on the safe side. Untreated eye injuries or infection can actually lead to blindness, so having it looked at as soon as possible is the way to go.
I hope this helps.