I'm 6'5", and I weigh 242lb, for a BMI of 29. (Overweight is 25, obese is 30.) If you looked at me, you'd never guess I was overweight - the most you'd see is a little excess belly fat if I took my shirt off. On the other hand, I bench 170, squat 200 and press 120 (no deadlift due to back injury). When I hit 253, I'll be obese, just like pretty much everyone in the NBA. Yes, I know my squat is low.
And, like most people in the NBA, I'll be eating just as much as any fat guy. That's what gaining muscle buys you - it lets you eat as much as ever while being "that jacked guy" rather than "that fat guy".
This also ignores the fact that to build and maintain the muscle, you are burning calories anaerobically, the same as you would if you were sprinting (slower running burns fewer calories, since it's primarily aerobic).