The crucial point here seems to be the acceptance of vilification if the person being vilified has any kind of CHOICE about thier situation. In this case fat people are seen as being in FULL control of their body shape while people don't have ANY control over their racial or sexual identity. There is no choice.
But we forget that there are implicit choices made when it comes to racism and sexism. The racist might honestly claim that they will easily tolerate the black man who dresses "white", talks "white" fixes his hair, goes to his Church in his part of town and doesn't make trouble.
The racist in this scenario is driven to fury when the black man CHOOSES to ride on a bus, or protest, or grow a "natural" hairstyle.
Likewise, a sexist might tolerate a woman working in his office; but if she CHOOSES to wear anything other than a modest skirt, she will incur his wrath.
Heck, sometimes there's even a crossover prejudice between race and bodyshape. How's that for making things complicated? A thin Samoan, who ever heard of such a thing? A fat Japanese person, they MUST be a Sumo wrestler.
So in the end, yes if a fat person is highly unhealthy, they would be well served to improve thier health, just as all people in such a situation would - but what possible reason or justification is there to make their lives hell?
And, if you're truly worried about the strain on the national health budget; why not seek out and berate a person who is skinny, sedentary and unfit rather than rolling your eyes at slightly overweight person who may be fitter than you are?