There is some disagreement in the medical community on this. There is some assertion that obesity was classified as a disease in 2013, primarily to allow healthcare providers to be reimbursed for time spent counseling patients on lifestyle aspects of prevention.
Merriam Webster defines a Disease as: "A condition of a plant or animal body or one of its parts that impairs normal functioning". Based on this, obesity can be considered a disease at the point it negatively impacts normal body function. We can all relate to it is a precondition for other diseases like diabetes, heart disease, back pain and certain types of cancers.
That said, I personally take exception to the morbidly obese (or alcoholic or drug addict, for that matter) who will deflect personal responsibility for their conditions by conveniently complaining "it's the disease", while continuing to willingly engage in the behavior that caused the problem. IMO, in such a case, the underlying "disease" isn't truly a physical malfunction, but the manifestation(s) of a mental one.