Weight gain in the American population 1960-2000

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103. Aspartame probably plays a role.

http://en.wikipedia.org/wiki/Aspartame
It was approved by the FDA in 1981, and it has been shown to cause weight gain unrelated to caloric intake:

http://www.sciencedirect.com/science/article/pii/S0195666312004138

Abstract

It has been suggested that the use of nonnutritive sweeteners (NNSs) can lead to weight gain, but evidence regarding their real effect in body weight and satiety is still inconclusive. Using a rat model, the present study compares the effect of saccharin and aspartame to sucrose in body weight gain and in caloric intake. Twenty-nine male Wistar rats received plain yogurt sweetened with 20% sucrose, 0.3% sodium saccharin or 0.4% aspartame, in addition to chow and water ad libitum, while physical activity was restrained. Measurements of cumulative body weight gain, total caloric intake, caloric intake of chow and caloric intake of sweetened yogurt were performed weekly for 12 weeks. Results showed that addition of either saccharin or aspartame to yogurt resulted in increased weight gain compared to addition of sucrose, however total caloric intake was similar among groups. In conclusion, greater weight gain was promoted by the use of saccharin or aspartame, compared with sucrose, and this weight gain was unrelated to caloric intake. We speculate that a decrease in energy expenditure or increase in fluid retention might be involved.

However, it's probably not a single-factor change. A set of factors seem to have converged around 1980 that contributed to this change in the slopes of the curves that you describe. Likely candidates include the introduction of aspartame, the beginning of the FDA/AMA/NHLBI "War on Fat" (resulting in excessive refined carbs and gluten/gliadin in processed food, that in accelerated the spread of metabolic syndrome), and advertising-driven changes in dietary habits ("May we supersize you?&quot

IMO it's unlikely to have been changes in exercise habits among children, as the increase in obesity is seen across all age groups. While the overall reduction in physical activity probably plays a role in the overall increase in obesity, I can't imagine how a gradual trend like that would contribute to an abrupt kink in the curves in 1980.