In fact many food contest champions are actually quite skinny. How much a person eats or how fast they eat don't neccesarily relate to how much the person weighs. Diet and exercise have more to do with their weight, and this often means what kinds of food they eat which is not neccesarily served at a contest.
Competitive eaters actually train to do what they do. But I don't think weight alone determines how well a person will do in an eating contest. Most of the participants work on conditioning their stomachs to be able to accept an increased amount of food and liquid, and learn how to control their breathing, how to combine food and liquid to get the most consumption etc. Those things aren't weight related.
No, I don't think a person's weight has that much to do with winning an eating contest. I'm thinking specifically of hot dog contests. In recent years, these have been won by petite, slim people. I've also seen very slim winners of pie-eating, pizza-eating, and egg-eating contests. These instances show that weight is not a factor.
Just because a person doesn't weigh all that much doesn't mean they can't consume insane amounts of food. The hot dog eating champions and noodle eating champions are frequently perfectly average sized people, not gluttonous behemoths. Competitive eating requires a form of conditioning, just as any extreme endeavor does, and being a lazy lard bucket doesn't really lend itself to discipline.