Firstly, it might simply be that keeping your eye open to watch TV, while lying on that side of your face, simply stretches the tissue around the eye, causing it to water.
Alternatively, it could be something as simple as dust mite debris in the pillow/cushion, which you're lying on, causing irritation in the eye.
For either cause, the solution might be to switch to another (preferably new) pillow or cushion.