my westie pup is 13 weeks old, and has wet eyes, sometimes running a bit, my vet did not seem at all concerned and gave me nothing for it , any ideas what might be wrong

Sometimes if the hair has not been trimmed around the eye the hair can get in the eye and cause iritation.  Maybe worth trimming it. ( use round ended nail scissors though) 

You could try wiping the eyes a couple of times a day with water (boiled to kill any germs and then allowed to cool before use). Use cotton wool balls and use a separate one for each eye discarding it after a single use.

If no improvement after a  couple of days then I would go back to the vet (or seek the opinion of a second vet if necessary). Eyes are too precious to take chances with.