There are there reasons why our eyes come out of water. First, when our eyes face wind or cold air or some else directly, our eyes will come out of water because eyes must make sure there are nothing in our eyes to stop them works. Second, it can be caused by external injury, trachoma, conjunctivitis, inflammation of nasal cavity and eyelid diseases. Third, it can be caused by atrophy of lacrimal sac muscle. I think your eyes start watering is because your eyes face wind or cold air directly by accident, so it has nothing to do with meditating. It is very common, so you don't need to worry. It is ok. If you still worry, you should go to see a doctor.
Watering eye is a condition that eyes produce too much tears onto the face, also know as tearing or epiphora, until now, scientists and doctors can hardly explain why. It's said that there are many reasons that can cause of eye watering, including disease, a blocked tear duct is the most common cause, but there are a number of other causes, and especially for the older people, watering eyes is a common problem, so it's hardly to explain why your eyes start watering when you meditate, I suggest that you'd better see doctor and check up why.