Obese is different from being heavy. I will agree with the above quote, but just how much will this impact a real fight? Usually, martial artists do not run after people to fight them - they come to us, so running performance is irrelevant. If my opponent is too tall to reach with a head kick, I'll kick/punch them low, so vertical jump ability is irrelevant. Aerobic capacity will not be relevant, either, as the fight won't last too long. At least these things are true about the 250 pounds and over blackbelts (most but not all Pacific Islanders) I've been acquainted with. They were really quite scarry in combat.