Fresca, there's no such thing as a 'typical' vegetarian. Body conformation has far more to do with genetics and the metabolic set-point established in late childhood / adolescence than * it actually has to do with adult food choices. (That's not saying that eating 10,000 calories more than needed won't make someone gain weight, but two adults, both eating nutritious, complete diets with the same calories and fat grams, one vegetarian, one omnivorous won't respond the same way. It's not as simple as 'Good'** Food = No Fat, or even balancing calories against activity level.
Moreover, food choices and obesity have less to do with general health and longevity than common wisdom would have one believe. There are obese, diabetic vegetarians and rail-thin junk food junkies; 80% of heart disease and diabetes occur in people with normal or low BMIs.
* Which is why it is especially dangerous for young women to diet; they're artificially lowering their metabolic set-point and setting themselves up for a lifetime of fighting to conform to societal preconceptions of F#$%ability.
** Not that 'Good' Food is defined at all well. It probably means minimally processed, high in fiber, meat from animals not CAFO'ed, but that's a religious argument.