The rising levels of obesity have been declared a global epidemic by the World Health Organization, with obesity rates surpassing 50% in many countries. Between the late 1970s and the early 2000s in the U.S., the prevalence of obesity doubled while the prevalence of severe obesity more than tripled. One of the factors underlying the obesity epidemic is secular changes in activity patterns due to an increasingly sedentary lifestyle. A better understanding is needed of how daily activity patterns relate to obesity. In this study we use wrist-worn accelerometry from the National Health And Nutrition Examination Survey (NHANES) data set to develop a number of features that characterize daily activity profiles, as well as fluctuations in those profiles over time, and determine how those features correlate with body mass index (BMI). Using a data set of 2,882 subjects split evenly between a training and test fold, we constructed regression models that estimate BMI based on activity profiles and fluctuations. We found a correlation of r=0.47 between estimated and true BMI, resulting in detection of overweight, obese, and severely obese subjects with area under the ROC curve (AUC) of 0.69, 0.73 and 0.85. These results indicate how patterns of activity levels across daily sleep/wake cycles are associated with higher risk for obesity.