Tear staining is one of those topics where there is unfortunately no single magic fix — because the reason dogs’ eyes water can be completely different from one dog to another 

• Sometimes it is related to food sensitivities or allergies, and changing the diet can make a huge difference. Very often these dogs will also show other signs such as paw licking, itchy skin, ear irritation, or general skin problems.

• Sometimes it is environmental — for example grass allergies — and reducing exposure helps.

• Sometimes the issue is connected to the gut microbiome, and probiotics can improve it surprisingly well.

• In some dogs, tap water itself can contribute, as certain chemicals or mineral content may irritate sensitive dogs. Some owners notice improvement after switching to filtered water.

• If there is a bacterial infection involved, then a veterinarian may prescribe antibiotic eye drops.

But not all general practice vets are equally experienced with eye problems in toy breeds. If basic treatment does not help, it can absolutely be worth seeing a veterinary ophthalmologist or another specialist for a deeper investigation.
And sometimes the problem is structural rather than “cosmetic”:
• an eyelash growing inward 
• a slightly rolled eyelid 
• a tear duct issue 
In those cases, surgery may be the real solution.
It is also important to understand that structural issues are not always simply the result of “bad breeding.” Genetics absolutely play a role, but many of these traits are complex and polygenic rather than directly inherited in a simple predictable way. Biology is unfortunately rarely that straightforward.
And of course daily hygiene still matters regardless of the cause — keeping the eye area clean and making sure hair is not irritating the eyes can make a big difference too 
This is also why I am always cautious when people advertise miracle products for tear staining. 
The stains themselves are usually just a symptom — the important part is understanding why the eyes are watering in the first place.