It's abnormal for the kid's eyes water while watching TV. Because of the fatigue of eyes, it will get dry eye, tears, eye swollen, sore eye or blur vision symptom later if you do not pay attention to this situation. This is just because long time use of the eyes to watching TV. The screenshot are too dazzling to the little kids, and it hurts the visual purple to makes color cast and hurts the visual pigments. The kid likes watching TV while running, which will make kids feel dizzy and hurt ciliaris for a long time, then lead to myopia. You'd better take care of your kids, binding the time of TV watching and make sure the TV in modest rays' condition.
No, it is not normal for the kid's eyes water while watching TV. It must be the reason that your child has watched TV for a long time without a rest. Thus, the tear gland gets tired and can't help watering. So you should control the time of watching TV for your child in avoid of the short sighted symptom.
While watching TV, your kid's eyes water maybe because her eyes is infected by inflammation, and there is the possibility of trichiasis or the obstruction of lacrimal passage. Do not let your kid keep watching TV for a long time, forty minutes each day is enough, and keep a distance to the screen, such as more than 2.5 meters. And also do not make the color of screen so bright. At the same time, she needs drink plenty of water and do not have too much spicy food for keeping eye health.