If you've ever seen someone crying, I mean really crying, you'll notice that often they have a runny nose too. Normally you don't see this when your girlfriend is shedding a couple tears when the guy in He's Not That Into You is proposing. Nor do you see a runny nose when you're shedding a couple tears because you realize you were dragged out to see the most convoluted, soap opera-esque movie...ever. You do however, see the runny nose if you see someone really bawling. Just find me if they ever make a sequel to He's Not That Into You.
You see the runny nose because our eyes are connected to our nose through a nasolacrimal duct. Tears flow from the lacrimal gland, which is in the upper outside corner of our eye, and flow downwards. Some flow out of our eyes and down our face, but a large majority flow into the lacrimal sac, which is that red, ball shaped sac at the inside corner of our eyes. That lacrimal sac is connected through lacrimal cannaliculi (canals) to the nasolacrimal duct, which is connected to our nose through paranasal sinuses. And that's the path tears take to run through your nose.
This anatomy is a two way street and explains how some people can snort milk up their nose and squirt it out their eye (seriously!).
I really hope they don't make a sequel...