The cause of your condition is the same as that of the ordinary watery eyes. Your watery eye is the result of the blockage of the empty pathway and excessive production of tears. The latter is related to irritation or dry eyes. There are other causes for watery eyes, such as Blepharitis, Conjunctivitis (pink eye), nasolacrimal duct obstruction, irritation and canaliculus blockage. Other factors including long exposure to the sun, lack of sleep, watching television and working on computer for too long can also lead to watery eyes. If you wear contact lenses, it may be because there are allergens and proteins sticking to your lenses. The other eye is OK because it is not affected by the factors mentioned above.
Many things cause watery eyes, like dry eye,trachoma, and so on.The tear drainage system may be plugged. Also, one of your eye may be infected by germs. The one which is always watery may have pink-eye. There is possibility for conjunctivitis.
Contact your eye doctor to be examined.
Since you find the symptom of only one eye's crying now and then, you should check out whether there is the problem for your tears glands system. It is really weird which you need to pay high attention to. Your eyes may get infection which may cause it. You need to have the good rest for the eyes and eat more food with vitamin C to moisture the eyes to make them feel comfortable.