My right eye is tearing a little since 6 months ago, not everyday but once per week. no pain, no irritation. what does that mean?

Get an eye exam: Although it is probably nothing serious, you should have an eye exam by an opthamologist in order to make sure, .

Dry eye tearing: Dry eyes can cause friction on the surface of the cornea and trigger a sudden release of tears. Lubricating eye drops can help with this friction prevention as they make the tears wetter, slicker and coat the cornea better in between blinks.