My Yorkie is also 16 weeks and he pees on average no more than 5-6 times per day. I offer him water only during his feeding which is twice a day. Trainers will tell you that puppies don't need that much water. If you leave the water bowl out all day, he will urinate constantly. You should offer him water only with his meals. Eventually, he will realize that he needs to drink as much as he needs in one sitting, and you will be able to control his peeing.
If you are not offering water all day long, you should call the Vet.
