When the hair is constantly wet from profuse lacrimation, it is a breeding ground for bacteria and yeast. One of the most common infections are yeast types: Ptyrosporin or Red Yeast, which cause deep reddish brown spots. Bacterial infections in the tear ducts can also lead to this result. 

Obstruction of the tear ducts
Can be removed only by a veterinarian ophthalmologist.
Ear infections
Ear infections can contribute to excessive tearing. Try to keep your dog's ears dry when bathing your dog. Tousled ear hair should be removed. Ear cleaner used: Nolvasan Otic http://www.1800petmeds.com/Nolvasan+Otic-prod1972.html
May protect clean ears and white hair.
Genetics
Heredity can have an impact. "Yes, and small dogs are closer to the ground and to the dust IMHO"
Changing teeth
Changing teeth has a great impact on lacrimation. Chew toys to relieve pressure on the mouth during this time.
Allergies
Try to keep the hair that grows around the eyes from getting into your pet's eyes.
Allergy can be caused by any means: cigarette smoke, various hair care products. Small amounts of the product can protect your pet's eyes:
DuoLube (Bausch & Lomb, USA)
http://www.prescriptiondrugs.com/drugs/duolube The
type of food can also cause allergic reactions due to inflammatory reactions in the gastrointestinal tract. An inflammatory response can change the pH of your dogs' fluid, which can lead to allergies.
Water
Use only purified water.
Food
Diet. I find that feeding dry food that contains no chemical additives, preservatives or food coloring will help maintain a white coat. Many commercial products contain cellulose fibers that can cause beard discoloration. I wrap my beard so that their food doesn't come in contact with their hair. If the beard is not wrapped, it must be washed continuously to remove any partially digested food.
Fleas

Fleas reproduce in a humid environment and their waste products affect lacrimation. Fleas are also carriers of ear mites. Ear mites can cause serious ear infections and tear stains as a result.