Obviously weight and fitness are mitigating factors in diver competence. Do the recreational technical agencies that teach mixed gas have any fitness requirements, or is it similar to an OW program where a person gets signed off by a non-hyperbaric physician?
I'm only really familiar with GUE and TDI standards, so can't comment generally.
GUE are probably have the most obvious standards. They don't allow smokers to take their courses (GUE instructors have the ability to strip certifications from people they see smoking after a course), they have swim tests for all their courses (surface and u/w breath hold) - though not overly onerous at the entry level, they get tougher as the courses get more challenging. For my Fundies course (which is <30m non-deco nitrox course) half the pre-reading was about smoking, health and fitness. I'm doing the Tech 1 (<57m normoxic trimix) early next year, and expect much the same - plus a good ribbing from the instructor.
What I do like about the GUE courses is that the instructors get in the pool and do the swim test with the students on nearly every course - the guy who is doing my course was the national fin swimming champion of Ireland, and I am a plodder when it comes to swimming. I always feel a bit jipped about timed swim tests as a result, but hey... you have to measure it somehow. GUE also allow holistic health and fitness evaluations by their instructors - taking into account alcohol use, weight etc etc.
TDI do not require any form of fitness evaluation as such for any of their courses, but they also don't preclude it. Most do, however, have skills that require physical fitness - e.g. tired diver tow (in full kit) on the surface and u/w, and an u/w breath hold swim (in full kit). TDI standards allow instructors to exceed the minimum requirements, so we have put in a big classroom section on health and fitness and tend to do swim tests for candidates we don't know. We do waive those for people who have done courses with us before who we know are exercising regularly and diving regularly.
I think the big difference between GUE and TDI is consistency. GUE only has 60 or so instructors worldwide, they all know each other and talk to each other regularly. They also have a recertification requirement (both for divers and instructors) so it's easy to keep quality under control. TDI are at a stage of their development where there are many instructors, and now many instructor trainers, which makes it more of a challenge to maintain some consistency in standard of education. From a potential students perspective, it makes it more important to shop around and find an instructor who will give the student what they need, as opposed to what they want.