As someone who has been morbidly obese, obese/morbidly obese are medical definitions, and they are subject to debate even in the medical community. No one really has any business using those words except (a) a person's medical professional or (b) a person who has received that diagnosis and chooses to accept and use the term. And they certainly should not be equated with the "neutral or positive descriptors" vibe the event was going for with "fat," they're literally negative medical judgments about a person's overall health prospects. They are laden terms. Not denying that what they're laden with has a basis in fact, but their place is in a person's actual health care, not in the parlance of strangers chatting.