I used to be kind of a _______ when I was little, but I lost most of the weight in my teenage years.

From the given sentence, we can infer that the author used to be chubby when he was little and lost some weight as he grew up. Therefore, the missing word should mean 'fat or chubby'.

Let us evaluate the options:

Runt is a term used to describe a small and weak person. 
Beanpole is a term used to describe a tall and lean person.
Punk is a term used to describe someone of little value. 
Doughboy is a term used to describe a chubby person. 

Therefore, doughboy is the correct term to be used and hence, option C is the right answer.