Excessive water drinking can be a sign of many illnesses, diseases, and problems. It can indicate thyroid problems, diabetes, infection, or problems with liver and kidneys (which yorkies are very prone to) to name a few. You should have your vet check out your pup to be sure. Any time you notice your pet drinking a lot of water or more water than they used to you they should be checked out.
My friend has a yorkie and they drink so much water because there bodys are so little, when they run around and have exercise they lose a lot of energy so they go and drink so much water.
I have the same problem with my dog. He is 12 years old now an drinks 3 big bowls of water everyday however this is a problem because he wee's in the house everyday. I'm to afraid to take him the vet because I do not want him being put down.