I use apple cider vinegar in my dogs drinking water and yes, it helps rid of the tearing. The idea is that it helps balance the ph in the dogs system. I have one dog that does have the tearing more then the other's and it has made a huge difference. I also use the vinegar and water as a final rince after bathing, it not only makes the coats nice, it is a natual flea repellant. Great to use on puppies or pregnant bitches.
My other furbaby is a maltese and her eyes get really bad in the fall and spring. I really like eye envy. It is a product you put on the area rather than feed. It takes a week or two if there is a lot of staining but works great. Just remember to keep it in the fridge!
I use a very small amount. About 1cc to a large bowl of water, sorry I don't know how much water the bowl holds, but you don't need to use much. Start off with even less then that, so the dog can get use to the new taste and smell.
I use the gallon size apple vinegar I get from my grocery store made by a generic company. The only ingredients is: apple cider vinegar and water. No need in paying big dollars for what a specialty has, as it would be the same.