I have not researched into this area but I can think of a few explanations.
1) Food prices have decreased due to globalisation which has lead to an increase in portion sizes and overconsumption. Food prices are much cheaper these days as globalisation has allowed us to grow and produce food much cheaper in LICs (low income countries). This means Americans are more likely to consume more food as it is cheaper.
2) Fat is not the only cause of obesity: In the 1970s-1980s the popularity of low fat "health" foods skyrocketed (and has maintained popularity to this day). To compensate for the lower fat the amount of sugar was increased. Sugar is as bad or even worse than fat when it comes to causing obesity so replacing fat with it does not stop the rise of obesity.
This is a very interesting question and I could write many many more hypothetical answers so this is just scratching the surface.
Hope it helps.
