For Medicare, the costs of obesity are about 72 percent greater just for prescription drugs, Finkelstein said. An obese person on Medicare is going to pay $1,400 in drug costs more a year than a normal-weight person, he said.or people on Medicare, average expenses for a normal-weight person average about $4,700 a year, while costs for an obese person range about $6,400 annually, Finkelstein said.