I think LAWL might imply it is only for young, hip, single people, at least in some people's minds. The name change may not be original, but it could be a smart mareketing move, especially in communities with a shortage of young, hip, single people.
Family Weight Loss, implies not only a broader target audience, but that the whole family should join together. Brilliant really, and if they further provide family perks, or a family discount (no matter how small), it could increase their profits tremendously. I always thought that WW and other programs would draw more couples and families if they did something like that.