Will being overweight mean I won't get the job with the brittish heart foundation I want?

ok so I have an interview to be manager of one of bhf shops, working for a charity is something i'm really pionate about getting into but I'm worried that because the specific charity promotes health & wellbeing, I might be penalised since i'd be working with the public & representing the company! (I'm 16 stone, female & around 5 foot 6 inches)Obviously they can't say that's the reason they don't offer me the job but if I was totally qualified in every other way, would my weight put them off hiring me, even if i'm on the road to losing weight & leading a healthier lifestyle?