Over the past five decades in the United States both total medical expenditures and the proportion of medical expenditures financed with public funds have increased significantly. A substantial increase in the prevalence of obesity has contributed to this growth. In this study we measure the external cost of obesity, in the form of publicly funded health-care expenditures, and how this cost changes when the distribution of obesity in the population changes. We use a continuous measure of obesity, BMI, rather than discrete BMI categories to represent the distribution of obesity and changes in it. We predict that a one-unit increase in BMI for every adult in the United States would increase annual public medical expenditures by $7.2 billion. This estimated public cost equates to an average marginal cost of $32 per year per adult for a one-unit increase in BMI for each adult in the U.S. population. Separately, we estimate that if every U.S. adult who is now obese (BMI 30) had a BMI of 25 instead, annual public medical expenditures would decline by $166.8 billion (in constant 2009$), or 15.3% of annual public medical expenditures in 2009. Assuming a socially optimal BMI of no more than 25, we estimate that the prevalence of obesity in 2009 resulted in a deadweight loss of $144 billion in 2009.