“We ask them, ‘What is the barrier?,’” said Akofa Bonsi-Wallace, the former director of discharge planning at the University of Alabama at Birmingham hospital, who often reached out to nursing homes in Georgia, Florida and Tennessee. “Most of the time it’s staffing. We’ve heard, ‘I already have a morbidly obese patient, and they are eating away at my staffing hours.’”

At the Generations of Red Bay facility, nurses reposition obese residents like Ms. Chism, who are unable to move on their own, every few hours to avoid dangerous pressure ulcers. Daily personal needs require monumental coordination. One nurse can help a resident of normal weight dress and sit in a chair within 15 minutes, said Kathy McCurry, head treatment nurse. “With a bariatric patient, that takes an hour with two certified nursing assistants.”

There are other reasons nursing homes are wary, including the inability to transport such patients to the emergency room, the possibility of staff injuries and higher workers’ compensation costs, and the infeasibility of remodeling older buildings with wider door frames and special plumbing to accommodate sturdier toilets.

The paucity of available beds has meant heavy patients can languish in hospitals, at great expense to Medicare, private insurance companies and the hospitals.

“We’ve had patients in the hospital for several months,” said Dr. Lynn Crawford, the medical director of the University of Alabama at Birmingham Hospital-Highlands geriatrics unit — an observation echoed by other hospitals and national industry groups.

Martin Bayne, 65, who has Parkinson’s disease and weighs 370 pounds, found himself stuck in a hospital in Pennsylvania after episodes of congestive heart failure and the flu. “It was hell for me,” he said, lamenting the helplessness and humiliation he felt awaiting placement in a skilled nursing facility.

“There’s a terrible feeling that goes along with knowing that you’re not wanted,” said Mr. Bayne, an advocate and blogger on issues of aging. He now lives in a personal care home in Center Valley, Pa.