Depends. I know someone someone who lives in a not-exactly cheap area in Central London, and openly admits that if he was to get employment, he'd lose the benefits and wouldn't be able to live in such area, so he might as well not bother. Not exactly a praiseworthy attitude surely?
I don't mind people getting subsidies/help for getting a roof over their head, in fact I didn't say anything about the idea of coaching. However, I have an issue of giving people what I consider to be luxuries (see next).
When I say privilege, I mean luxury. Luxuries are not necessities. A brisk walk down the street, kicking a ball in the park, rope skipping, pushups, there are plenty of exercises one could do without going to the gym. Yes, gyms are nice, comfortable environment (for what they are), but that's exactly why I see them as luxuries rather than necessities. I just don't see why people should be pampered for not taking care of themselves.
What I am thinking is, does it really have to be a gym? Based on how much they charge, it can't be cheap to build/maintain. Given that you can lose weight/build strength using some of the methods previously listed, wouldn't you save even more taxpayer money?
Sooner or later they are going to have to learn not to be so self-conscious (in my eye few people including myself are "perfect-bodied"), and exercising in public will help with that. In this relatively PC society, anyone who points and laugh at overweight people exercising in the park are more likely be the ones getting shunned. People like to root for the underdog, and also, they are probably going to appreciate seeing that overweight who are genuinely trying and breaking their habits.
You can't shelter insecurities forever, let's say they graduate from a gym for overweight people with a BMI similar to yours (normal range). They go to a 'normal' gym and see what you see, feel worse than you feel (insecurities is all in one's head), then retreat back to their home leading to a relapse. Wouldn't that be a waste? And of course, you can't keep them in the overweight gym either, since you'll then put off those who are 10 stones overweight.