In my youth I knew a really obese guy, about 6 feet high, who could kick the buzz of anyone in high school. He could really carry a big load as well. The way I see it, body fat is not part of your carried weight as less mass is also less muscle. Only in extreme cases where you are completely static, will the body be prevented from developing the muscle needed to carry that extra mass. In modern life this is possible as a guy could be on welfare, only daily exercise would be walking to his car, driving it to the nearest fast food outlet. In a medieval society, that guy would be dead. Or he'd have enough muscle to carry his fat walking to a marketplace, probably miles away, that hardly had any fatty food to offer at all. Being really fat and physically handicapped by your fat means your ST stat have seen no action and is parked at 19 with no stat gain in sight, IMHO.
Sumo Wrestlers should be an example of high ST fatty people. Incredibly strong, incredibly obese, actually pretty agile, some are even quick. But they eat a ton of food every day and still exercise alot. Then they usually die early, often from heart failure, but that's a different discussion.