Weeping eyes can be the result of tooth root problems. Unfortunately, not much can be done for that. It would be a good thing to know (via x-ray), especially if the vet is concerned about a possible abscess. However, if you’re not ready to go that route, you could try treating the symptoms to see if it helps. You could try a warm compress on the eye to see if that helps open it up a bit. An anti-inflammatory medication may also help.
Is she eating normally? Does she have any other symptoms like sinus problems, head tilt, facial paralysis? Usually with tooth root problems, you see more than one symptom because the eyes, sinuses, and ears are all connected. This isn’t the case 100% of the time though, of course.
There are other things that can cause a blocked tear duct. Dwarf breeds, for example, can have congenital defects in this area because everything is “smooshed”. URIs can cause a blocked tear duct as well.