Do you burn more calorie if you are more fit?

No. obese people have a lot more fat on them than people that are working out. So if you're working out and you're fit then you are going to lose more and look a lot skinnier than the obese person... and the obese person needs to work a lot harder then the person who's fit because they have a lot more to burn off.

Alternative answer:

By the fact that an obese person weighs more, and has a larger body to support, it is a logical assumption to make that an obese person 'needs' more calories to maintain the same weight.

However, the amount of muscle mass a person has will also dictate how much energy is used, and this may vary substantially between obese people.