Well, in my opinion, it is possible for your eyes to have tear running out. So you do not need to worry about it. On the other hand, for your watery eyes, it can be annoying and dangerous. First, you should know that watery eyes can be a sign of dry eyes. Generally speaking, tears are for lubrication and for keeping your eyes clean. And when your tear glands don't work in a wrong order, it may develop dry eye syndrome. At that moment, the tear glands react by producing large amounts of tears. And that can lead to some symptoms which just like you had. Also, in some cases, allergies and eye infection can also cause watery eyes too. So just check your situation as soon as possible.