If you've got 250 grand plus you don't mind losing then go for it.
There simply is not the market or demographic in a single catchment area for WLS patients. Your gym would need hundreds of members to make it viable and you would not get anything like that if you restrict it to WLS patients. Add in the current economic situation and you see open access gyms closing not new ones opening unless they are the big brand gyms. The Olympics will result in a surge of new members who will sign up and go for the obligatory month before they lose interest but it will not be enough to sustain a new gym, and certainly not wLS post oppers.
Gym quality equipment pieces are around £500 each and you'd need plenty to stock a gym. Add in weights and racks and mats etc and your start up costs could be fifty grand for all the new kit people want to see. Add in premises, staff at £!5,000 plus each, insurance, rates, utilities, and you can see where the money goes in the first year. In the second year you have to have kept up the membership replacing the drop outs from year one.
Gym ownership is a tough business in any application, to try to restrict it to just one very specific member type is just not viable. Sorry to rain on your idea, which is a great concept but one that would lose you a shed load of money