What is the term little meatballs (referring to spoiled kids)?
From my life experience, there's no such phrase as "Little Meatballs". 

What children (or even some adults) use to make fun of overweight kids is "小胖墩". "小胖墩" literally means "Little Fat Chunk", and of course, it is a slang word. And here, it is more likely "小胖墩" is used to represent children been spoiled with foods since s/he is the only child.