Well, for some people, it can be a normal situation. And generally speaking, when you brush your teeth, the paste can just stimulate your mouth, which is connected with your eyes. In that way, your tear system will be stimulated by paste too. And then it will just lead to watery eyes. So we can say that it can occur to some people. But if your eyes become watery heavily, I have to say that, there is something wrong with your tear system. And you may need to see the eye doctor as soon as possible.
Check if you still shed tears when you change the brand of your teeth paste. I will say, there may be something wrong with your teeth paste. Is there any irritant material or ingredient inside the teeth paste? Find the cover and read the instruction and ingredients. Does it contain something you are allergic to?
That is something you do not need to worry about. Many toothpastes have peppermint in ingredient to make your mouth fell good. However, peppermint can be easily volatilized, which will get in your eyes according to the principle of proximity.The peppermint molecule in your eyes can be a stimulation to induce the tears.
Hope that will help.