The aforementioned high food availability and cultural habits can enable this, but aren't sufficient to propel it to this epidemic scale. The biggest factor now is profit motive. Not on the eater's part, obviously.
I'll try to put it in simple terms. Imagine a given population who average a healthy weight. You're trying to come up with a product to sell, but can't see a niche available, until it dawns on you that if these people would eat more, the market for foodstuffs would see a significant increase in demand with seemingly no downside. It would be akin to a completely untapped market just waiting to be exploited, and one which brings no extra problems. Except it does cause a lot of problems, but they don't figure in the bottom line of any processed food manufacturer. It's a not-at-all-classic case of society bearing the collective cost for the benefit of very, very few, a peculiar twist on the tragedy of the commons. Even if you were to consider the volume eaten to remain constant, this would still happen, because the profit motive also leads the manufacturers to come up with products which prioritize almost nothing but taste, which, by definition, plays to unconscious weaknesses in our part. It's a cliche to say, but no less true because of it, that sugar is addicting, because of evolutionary factors which have since changed completely. Our ancestors prized these then-rare foodstuffs because it was an advantage to seek out these calorie-rich things. Now that it's not rare, well, you get the picture. Capitalism inevitably engenders a society of unsatisfied and frustrated people, because these make for more consumerism.