Well, with any gene, it takes the proper environmental factors for it to be expressed. So while very few people would argue that height isn't largely genetic, most people also accept that it takes proper nutrition in order to grow tall. So even though height is genetic, and South and North Koreans largely share the same genetics, South Koreans are way taller than North Koreans.

The genetic argument for obesity is that in areas of occasional famine, it made evolutionary sense to horde food in your gut, particularly fatty food. Until very recently in human history, there just wasn't that much fatty food for your average citizen to horde. Now there is, particularly because food corporations have realized over time that the fattier the food, the more of it they sell, and those previously advantageous genes are running amok. Not everyone has those genes because in places of plenty, those genes aren't that advantageous.

I'd agree that that isn't an entirely convincing argument. But I do think it's part of the story.