If a cat frequently sheds tears while eating, it's usually due to congenitally narrow tear ducts. In this case, the cat's health is generally fine, and the owner just needs to regularly clean the cat's tears.
Excessive tearing can easily lead to bacterial and fungal infections, causing symptoms such as excessive eye discharge and red, swollen eyes. After treating your cat accordingly, it's also important to maintain a clean environment to reduce the risk of bacterial infections. 
It's also possible the cat's food is too salty, or it might not be drinking enough water, causing it to become dehydrated. Alternatively, the food might be difficult for the cat to digest, leading to hormonal imbalances. Finally, the cat could have an eye condition, such as conjunctivitis or keratitis. Observe the cat's condition closely and take it to a veterinary clinic for treatment as soon as possible!
