You are talking about two different issues. I never said it was acceptable for the child to say what they said. I think they should be punished but at the same time the parent should figure out where they got the impression that anyone doesn't have to listen to anyone else because of their weight. The notion that authority and weight are related makes no sense in most scenarios.
The second issue is the actual weight of the person. The standard of health in this country is appalling and a big part of it is the expanding waste line of the average American. I believe that despite what the media likes to say about actors and athletes the first and most important role model in any child's life is their parent(s). A big part of being a good role model for your kids is to set an example. If you don't want them to swear don't swear. If you don't want them to be dishonest don't be dishonest. If you want them to live active lives and eat healthy, live an active life yourself and eat healthy. Not a single one of my active, in shape friends have inactive, overweight kids. Not one. So yes, the weight of a parent in this situation is very important to how their child not only portrays them but also how they portray themselves.
The OP had no context to their post so it is hard to give an accurate judgment. If the parent said to the kid they need to do their homework and the response was "I don't have to listen to you because you are fat" that makes no sense. However, if the parent was yelling at the child about their lack of physical exercise and poor eating habits while at the same time spending their free time sitting on the couch watching soaps and eating tubs of ice cream I think they would be hypocrites. The same reaction by the kid might not have been communicated very well but he/she would have a point.
These things always turn into flame fests but I am not going to pretend I feel a way I don't. I don't care if someone is or isn't fat any more than I care if someone is or isn't bald or anything else you want to insert here. I have friends that are obese and others that have abs you can do laundry on. I do find however that people who are unhappy with themselves love to attack positions like mine out of some sort of misdirected rage. Either be happy with how you are or change it, those are the two options in life.