Hmmmm, whether or not there is a gene linked with obesity, it's not rocket science. Any animal can only gain weight, and remain overweight, if it is allowed to do so by over feeding. I was told at the first show with my home bred pup that I wouldn't get anywhere in the show ring with her unless I put more weight on her. She was (is) a perfectly healthy weight, yet the judge didn't even look over her properly, as she was too skinny. Now if she were really too skinny, surely it should have been reported to a vet? I do think there are a lot of excuses made for some dogs, and the show ring is one place where some completely contradict themselves, fit for function, but with extra weight?
Photos are of mother and daughter, both predominantly show lines.