Just as a question - because I don't know the answer, not because I am trying in any way to be goady - are there disabilities which it would be OK to see as being incompatible with teaching, or is it illegally discriminatory to suggest that any disability would be incompatible with the job?
I was thinking, for example, about sensory impairments - would it be discriminatory to prefer a sighted teacher to a blind one, or a hearing teacher to a deaf one?
Rightly or wrongly - and I absolutely agree that it might be wrongly - I can see that schools would be completely prepared to make reasonable adjustments for a teacher with a permanent or acquired physical disability - e.g. someone like my grandfather with polio who was a wheelchair user, or someone who used walking aids after specific cancer treatment - that they might not be prepared to make for someone who has seriously impaired mobility simply due to their obesity.
That might be truly, genuinely unfair on the individual concerned, but it is a view that the OP might encounter, both during training - which would have to be in 2 different key stages - and perhaps when finding her first job.
Once a school has accepted her and made reasonable adjustments for her, it would almost certainly not impair her performance as a teacher (especially if the reasonable adjustments included e.g. swapping with a colleague for PE), but it might present a real or perceived barrier to initial entry to the profession.