[mscat]

Since you already have him, and he is ill, please take him to the vet fast! . He is young, tiny, and can die very easily. He is in a fraglie state, his health is not good, and his little body may not be able to fight off what is causing him to be sick. He is too young to have had all his vaccinations at 2 months old. If he has only vomited once, and has not had Dierreah then it is a better sign, however, being so young, I would still take him to your vet.
Because of his young age, and that he is a Yorkie , he may develop serious behavioral issues later down the road. Hopfully not. Right now, his health is the primary concern. Science Diet is not a good food as someone has aready mentioned. GO to the Health and diet thread and look under the Food LIst. There are excellent suggestions on high quality foods to feed, or feed homemade/but, You have to be careful with that making sure the puppy is getting all the right vitamins and nutrients.
A high quality Puppy food is best at this age free feeding .Your baby may be going too long in between feedings therefore eating too fast, gulping down the food than getting sick... He is starving by the time it's meal time. LIttle Yorkie's can only eat so much their bellies are so little, then they are hungry faster then a bigger dog would be, this is why it is easier just to free feed, esp, when they are so young and fragile . Your puppy is more likely going to over due it when he is starving at meal time then when he is not.
PLease get him on a high quality diet. What he is eating now is very poor. A yorkie does not eat much . Spending a little more on food , is worth every penny when it come to the health a quality of life . Your puppy deserves a good start in life. Also, he is going to need to start over in vaccinations.