Excessive tearing usually happens when your eyes are tired and irritated - not so much from the direct light of the screen, but because when you're looking at your phone, you blink way less than normal. You're staring for hours and your eyes dry out, so your body responds with reflex tearing to compensate. It's a protective mechanism that unfortunately becomes annoying.
What you can try: adjust the brightness so it's not brighter than the space around it (no need to go overboard with auto brightness), and more importantly, every 20 minutes or so look away and focus on something far away for at least 20 seconds. Sounds simple but it actually works. Also, if you can, increase the distance between your eye and the phone a bit - even just a few centimeters helps. If the problem gets worse toward evening, it could also be dry air around you or your eyes already being fatigued from looking at other screens during the day.
One more thing: in your settings there's usually a reading mode or blue light filter that reduces perceived eye strain. It's not a magic solution, but combined with taking breaks it helps a lot. If after a week or two of doing these things it doesn't improve, it's worth getting a checkup with an eye doctor just to rule out anything else.