I know not everyone will support my idea, but I truly believe I have an opportunity to start a unique business that will also benefit society in a very important way. I fully intend on trying to get it up and running in the near future.
Good for you for following your dreams, but from what you posted, I think there are a few things you should consider, imho, as you make your plans.
Your business model isn't precisely unique.
As stated above, Planet Fitness caters to beginners and actively discourages more advanced athletes. PF doesn't distinguish between the overweight beginner who wants to burn off some pounds versus the skinny beginner who wants to put an inch or two on his biceps. It's all about providing an experience free from "intimidation" for any beginner.
By making your membership exclusive to overweight people, you are by definition drastically reducing your pool of potential clients. My experience of many years training in the gym has been that overweight people often start out great guns, but lose interest after a month or two, meaning they have to be replaced fairly often to keep your cash stream flowing. By eliminating a large source of potential clients, you make that task a lot more difficult
Keeping the formerly overweight is also problematic. When an overweight guy walks into your gym, what he will see is a gym full of mixed overweight and normal weight individuals. You can tell him that they were all formerly overweight, but it still won't change the fact that he has to come in and workout with skinny guys. It might even make the feeling of intimidation worse, knowing that these guys have made so much progress and he has so far to go. BTW, I have witnessed many formerly overweight folks become openly contemptuous of the currently overweight. In any event, you have to understand that the business is catering to self-conscious, insecure people (fat guys who don't care will go to a regular gym)--anyone on the floor who they perceive as "better," no matter where they came from, will be intimidating. The idea is to eliminate the fear factor that prevents these folks from getting into the gym.
Planet Fitness works this into their business model for a reason. Let's say you walk into PF 150lbs. overweight and not able to bench press 100lbs. Then you work really hard, lose the fat, gain a bunch of muscle and get to the point where you can press 315lbs. If you do anything might might be construed as intimidating--such as grunting on your tenth rep of 315--the "Lunk Alarm" will go off and, if repeated enough times, your membership will be revoked. This is done so as not to confuse the potential clients who come by and would be intimidated by seeing a real bodybuilder, even if he was just an overweight schlub previously. Rather than celebrating that guy as an amazing success story, they actively discourage his participation because he has become what the gyms tells potential clients they exclude.
I am no fan of PF (any gym that has Free Pizza Monday as an enticement is a disgrace in my book), but they are an established franchise that appears to have largely the same goal as you to some degree. Have you looked into buying into a franchise rather than starting from scratch?