In fact, tears of the people are all the time to produce, however, you will not feel the tears flowing, because, your eyes have nothing special. But, if you have rhinitis or trachoma you may suffer the problem just like you have said before. If, it is not the case, so, your attention, it is a warning of your eyes. That is to say, you use eyes too much. Long-term such go down, you are not only in trouble what you have said, there are still worse things waiting for you. So, you need to pay attention to the rational use of eye. For example, in a period of time after the nets, you had better to close your eyes for a rest, if it is, you will feel comfortable a lot.
You may have the eye problems. The tears come out because of the excretion of tear gland which can be usually controlled. However, your problem may belong to the infection of eyes which may be caused by long time use of eyes in front of computers or high stress and so on. You'd better take notice of it and go to see the doctor as soon as possible.
That does happen to me also but not all the time. I tried once to find out why but it may be just because of the way you are lying down and the angle you are at. Some people have moist eyes and some don't so when you are on your side it is easier to have tears fall from the corners of your eye if you have excess moisture there.