Interesting thread...
Gentlemen, I must be the devil's advocate on something. Several posters have run down overweight martial arts instructors in this thread and it is a separate "running down" of them for that reason in addition to their poor teaching of "martial" arts. I have to disagree with this to some extent.
Although I agree that an expert martial artist SHOULD be fit, there is no absolute criteria saying that fitness and ability go hand-in-hand. Three cases from personal experience;
1. One of my earliest instructors was a 1st degree black belt in both judo and shorin-ryu karate. He was overweight and had a bad back and bad knees (from old injuries, not from his weight). He was also incredibly tough-minded and technically competent. I, at the time, was young and fit but relatively inexperienced. I thought, mistakenly, that an old fat guy would be a pushover in a fight. Of course, a teenager's muscle density put me at a tremendous disadvantage in comparison to an adult man, but I didn't know that at the time. Anyway, the guy is still teaching and is fairly active. He is a very tough customer and has proven himself in any number of fights, both in the dojo (striking and grappling) and in the "street". He is strong and tough, though not fast, but he makes up for his lack of speed with timing and experience. He is definitely NOT someone with whom you want to tangle unarmed.
2. A fellow student studying a bastardized Muay Thai/karate/grappling/escrima/whatever style was a guy in (at the time) his late forties. He was overweight (though not grossly obese or anything) and had had an alcohol problem throughout his life (he was "reformed" and was a substance-abuse counselor). He could not, despite his best efforts, gain much flexibility or speed. Bemoaning this to the instructor, the instructor told him not to worry about it but to concentrate his efforts on the things that he COULD do well. He also said (and rightly so) that attitude/mind-set was the biggest component of fighting, anyway. The old student was heartened by this and took it as something of a revelation. He concentrated on what he COULD do well and excelled. A very tough individual with strong will (curiously enough, given his history with alcohol), he was NEVER in good physical condition, at least to appearances, but he had almost unlimited endurance. He decided to run a marathon to prove to himself that he could and succeeded in finishing ahead of about 1/3 of the runners. He was intelligent and technically competent, proved himself in a lot of fights (he was a bouncer and skip tracer after my association with him), and was almost impossible to hurt.
3. A silat instructor of mine was crippled enough that he had to use a cane. He was not all that old (mid to late forties, I would guess...I never knew) and wasn't fat but wasn't in what could be described as "good" physical condition, either. I found out later that he was terminally ill when I knew him but I didn't know it at the time. He watched classes, mostly, and let his senior student run them with pointers when needed. When a point needed to be proven or shown (this was a rough class in terms of pain), the instructor would sometimes stir himself and perform the technique himself. He was American but had lived for years in Malaysia and the Phillipines and was used to a rougher environment than what most Americans see and saw no problem in actually doing unstaged things. Unlike most martial arts classes in which I've been involved, there was little or no "set" sparring or "one-step" sparring or anything like that. The instructor and his senior student were perfectly capable of performing pretty intricate techniques regardless of how you attacked (in other words, you didn't have to intentionally present a target for them to demonstrate). To this day, I haven't seen anyone better than this particular individual in performing locks, finding pressure points, doing throws or any other contact-range techniques (plenty of better punchers and kickers, but that wasn't his style) and he was definitely NOT physically fit.
Anyway, it's not that I disagree with instructors needing to be fit, it's just that physical fitness is no guarantee of knowledge or prowess just like not being fit is no guarantee that that knowledge and/or prowess is not present. Endurance is great and all but doesn't matter much in a fight that's over in a few seconds.