The adult obesity rate is "the percentage of the adult population (age 20 and older) that reports a body mass index (BMI) greater than or equal to 30 kg/m2." The data comes from the table listed as County Health Rankings National Data.
All data are for the counties in which the cities are located, except for Baltimore, MD. Thus the rate given for Chicago is actually the rate for Cook County, the county in which Chicago is located. New York City is the average of Manhattan, Brooklyn, Staten Island, Bronx, and Queens.