In the last century, U.S. diets were transformed, including the addition of sugars to industrially-processed foods. While excess sugar has often been implicated in the dramatic increase in U.S. adult obesity over the past 30 years, an unexplained question is why the increase in obesity took place many years after the increases in U.S. sugar consumption. To address this, here we explain adult obesity increase as the cumulative effect of increased sugar calories consumed over time. In our model, which uses annual data on U.S. sugar consumption as the input variable, each age cohort inherits the obesity rate in the previous year plus a simple function of the mean excess sugar consumed in the current year. This simple model replicates three aspects of the data: (a) the delayed timing and magnitude of the increase in average U.S. adult obesity (from about 15% in 1970 to almost 40% by 2015); (b) the increase of obesity rates by age group (reaching 47% obesity by age 50) for the year 2015 in a well-documented U.S. state; and (c) the pre-adult increase of obesity rates by several percent from 1988 to the mid-2000s, and subsequent modest decline in obesity rates among younger children since the mid-2000s. Under this model, the sharp rise in adult obesity after 1990 reflects the delayed effects of added sugar calories consumed among children of the 1970s and 1980s.