We have Caesar (on the left in the avatar) who is a 1.5 yr-old rescue dog (chihuahua-terrier, we think), nine pounds. The SPCA treated him for a bad case of mange before we got him, so his immune system definitely was challenged in the past. He had a rough go with kennel cough right when we adopted him, but has been healthy ever since (the last five months). We hope that with a healthy diet and a loving household (and age), his immune system has improved.
Our concern is that he tends to have teary eyes, that is, as if he had tears running down his cheek. Our vet said it was likely the dog equivalent of hay fever and to ignore it unless there was a suggestion of infection. We suspect that's likely the case, as we take both the chichis out for walks everyday if possible. Now that the weather has changed and we get out less often (too cold / wet / dark), the condition does seem to have improved but not gone away. It does not seem to bother him or be a serious problem, but if anyone has input we'd like to hear it. We believe strongly in getting our (otherwise indoor) dogs out for walks everyday, but don't want to be unnecessarily challenging Caesar's health.