morbidly tubby
When a person or animal is morbidly obese (has a BMI of 40 or more and is at a greater risk for illnesses including diabetes, high blood pressure, sleep apnea, gastroesophageal reflux disease (GERD), gallstones, osteoarthritis, heart disease, and cancer) but somehow retains a hint of cuteness.
John: Linda, your cat is stupid fat; she's struggling to breathe right now. It's kind of cute.
Linda: Yeah, she is morbidly tubby.
Linda: Yeah, she is morbidly tubby.