I have no idea why this is happening to you at night. It could have something to do with laying down which is creating these things to happen.
However, it is quite impossible to know what is actually wrong, without you being examined. There are two possibilities that you should consider: your tear drainage system may be plugged, or you may have dry eyes. Although this seems contradictory, these two conditions are the most common for causing watery eyes.
If your eyes are constantly watery, with tears dripping onto your face, I would suspect a blockage in your drainage system. This can usually be alleviated by flushing out the tiny tubes that drain the tears.
If your eyes water primarily when you are in wind or cold or when your eyes are irritated, I would suspect dry eyes as the cause. This can be helped by actually blocking the tear drainage system to keep more tears in your eyes.
I recommend you see an eye doctor who is familiar with lacrimology and can test you for these two problems, along with considering other factors such as your lids and how their shapes interact with your eyes.