My mom keeps feeding the family's cat far too much?!?

It's possible that his being sick is due to the overfeeding, but I think that if Tiger is really skinny and keeps being sick, you need to take him to the vet. He could could have some illness unrelated to the overfeeding. The vet will be able to tell you exactly what's wrong with him, and I think your mother would be much more likely to listen to a vet's advice than yours.