I feel like I might get flamed for this, but I just wanted to share my opinion... again, it's just my opinion and I understand where some posters here are coming from, but I have a bit of a differing view on it. To be honest, I feel like it's quite reasonable to have that in place.
As a healthcare professional myself (am a junior doctor), overweight (yes, my BMI is currently 28 and I started my journey at a BMI of 40 - definitely work in progress myself!), I absolutely understand why the hospital has put in a BMI cut-off point. There are public expectations of how frontline healthcare professionals should look like - this is inevitable and something I learnt very quickly as a medical student. Blue hair? Unacceptable. Eyebrow piercing? You must be joking. Of course, you could see it as discrimination, but you could also see it from another point of view - which is, whether we as healthcare professionals like it or not, appearance affects public perception of your advice/management. The cut-off for obesity as defined by the WHO is 30, not 35 - so people with a BMI of 35 are not just borderline obese.
I am definitely not of the opinion that there are no brilliant healthcare workers who happen to be obese around, but we also have to have a think about how effective it would be for a heavily obese frontline healthcare professional to talk honestly about lifestyle changes, impact of obesity on health, etc etc. This does NOT reflect anything on whether the obese individual is putting in any effort towards sustainable weightloss for him/herself (which obviously takes a long time as I myself can attest), rather on public expectations of healthcare staff in general.
Again, just an opinion, coming from an overweight healthcare professional - I thought it might be helpful for people to read something from 'the other side' (don't join us, we've got night shifts!).