Puppycow
Penultimate Amazing
People who got their stomach surgically reduced go from extremely overweight to normal weight, and stay there permanently.
Bariatric Surgery is successful, but not uniformly so:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1421028/
Yes, bariatric surgery seems to be the one intervention that could reasonably be called "a cure". A 93% success rate is really outstanding. Even the 57% success rate among the super-obese is nothing to sneeze at.
So, no obesity is not "incurable" but the cure is a rather drastic and expensive procedure.
The only other cure is a permanent lifestyle change, and some people can actually do that, but if you allow yourself to go back to old habits, the weight will come right back. For a few years I controlled my weight with a program of diet and exercise, but I had a rebound when I got lazy and went back to old habits. I'm not really fat enough for bariatric surgery though, but fatter than I should be.