As someone who writes a lot about weight loss and who was a fat (chubby?) kid, the problem here is that we aren't willing in our culture to call a spade a spade because we don't want anyone to suffer. This misses the point of life: it involves a lot of suffering. The trouble with "fat-shaming" in my mind is this--I believe most Americans have little control over being fat because our food environment has become toxic.
When I was 10, I had a doctor appointment after which my parents told me the doctor called me "corpulent" which my parents informed me was "one step away from OBESE!" I hadn't heard either word before but based on their tone, I could tell something was terribly wrong. But--no one offered me a single solution. Not the doctor and not my bewildered parents.
Half of Americans will be OBESE by 2030. Half. And I believe it's morally wrong to mock someone for a condition they have no control over (gender, stature, race, illness). To me, obesity is now on par with an illness. But there isn't anything wrong with DESCRIBING someone's gender, race, etc. And that is where this passage is a problem BUT you have to give the reader enough credit to know that the what is being written is an ugly stereotype, i.e. fat people just have no control over eating junk food. I'm not sure I've shed any light on resolving this but that's my 2 (maybe 3) cents.