Well you hardly need to be Kate Moss if you specialize in respiratory with geriatric patients, if you see what I mean. Physio isn't all about sports but on the other hand, I suppose it would be more reassuring for patients if you looked like you practice what you preach as a healthcare worker.
I'm not saying you need to look like an Adonis, but it does seem logical that healthcare workers look healthy. I watched Junior Doctors on the BBC and one of the FY Docs was obese - that strikes me as hypocritical but at the same time, he'd passed all his exams and made a competent doctor. But I wouldn't fancy buying a car from a man with a pranged old Reliant Robbin if there was another guy with a well looked after Ford Focus.
There'd be hundreds of nurses/doctors/physios etc who would be unemployed if you couldn't be overweight to practice. 'Looking healthy' has nothing to do with how good of a physio/nurse/doctor you are - whether that's weight or physical disability. I'd like to think the NHS (if you intend to work for them) wouldn't be so short sighted to rule you out based on appearance, but we live in an unfair world and no matter what laws and rules are in place, people will have opinions which may not be in your favour and sometimes those people can influence your chances of getting a job. Sometimes those opinions are totally irrelevant but an overweight physio does seem to fall into the same category as a nudist tailor or a vegan butcher - incongruous. But that doesn't indicate that they're bad at their job.
You can't be discriminated against, legally, but people can and do discriminate - especially when there's an obvious disharmony between the values of your profession and your seeming lack of those values.