I'll tell you what "fat privilege" is.
"Fat privilege" is never needing to go to the doctor because you know that regardless of whether something's actually wrong with you, you'll be diagnosed as fat and prescribed a diet, and sometimes told not to come back until you've lost 50 pounds. "Fat privilege" is the absolute certainty that whatever might be wrong with you can be cured by starving yourself, overexercising, having someone mutilate your stomach and/or intestines, or taking medications that can cause fecal incontinence or cause fatal damage to your heart.
"Fat privilege" is being treated to absolutely charming remarks made in a disdainful tone of voice about people who are about the same size and shape as you are as part of what was supposed to be a funny story about a friend's childhood. (And yes, I'm the author of that submission.)
"Fat privilege" is the fun of never really being able to be sure whether the person who's just asked you out is serious unless you know them well enough to know they're being sincere. Otherwise, there's always the chance that they're just playing a prank on you, engaging in a bit of sweat-hogging, or playing some variation of "Nail the Whale".
"Fat privilege" is the thrill of experiencing verbal, and sometimes physical, abuse for simply existing in public at your current size.
"Fat privilege" is the knowledge that a word that accurately describes your body has gradually picked up connotations of laziness, stupidity, ugliness, and worthlessness and is regularly used by people who want to describe themselves in those terms.
"Fat privilege" is the great honour of knowing that people who look like you are often used as visual shorthand for greed, overconsumption, wastefulness, thoughtlessness, sloppiness, gluttony, disease, aggression, laziness, stupidity, and carelessness.
"Fat privilege" is the joy of knowing that when employers write that prospective employees of theirs must be "neat and well-groomed" it's often code for "fatties need not apply". Furthermore, "fat privilege" is having an increased difficulty in finding work and earning significantly lower wages than our thin counterparts once we do get hired.
"Fat privilege" is not getting as good an employee discount as some other people because your employer has chosen to give a special reward to people with low BMI scores.
"Fat privilege" is being laughed at if you're walking, sitting, or leaning on something that breaks—perhaps especially if you're injured as a result. Hey, it's always nice to bring a bit of laughter into somebody else's day, isn't it?
"Fat privilege" is having a choice between precisely two options for clothing: the do-it-yourself option or the cheaply-made but expensively-sold option that's hideous, badly designed, and made of some horrible synthetic fibre fabric that will start falling apart after a single washing.
"Fat privilege" is the fact that so many people think that the contents of your cart or basket at the grocery store are somehow fair game for them to comment on or, in extreme cases, actually start removing while they admonish us that "You don't need to eat that!" And "fat privilege" is seeing the smirks on other customers' faces when they see that no matter what else you've decided to buy that day, you've also got some kind of junk food in the day's shopping.
"Fat privilege" is the ability to attract negative attention regardless of where we are or what we're doing.
"Fat privilege" is being told that all that we have to do to
"Fat privilege" is never being sure whether you'll have to purchase two airplane tickets for yourself—and knowing that if you do, there's no guarantee that you'll actually get to use the other seat, because it's likely that either the second seat won't be beside the first one or, because airlines routinely overbook their flights, they'll decide to put someone else in your second seat anyway.
(Note: Southwest is evidently not as horrible to fly with these days, and it's against the law to have a fat-people-must-buy-two-seats policy in Canada, but other airlines in the States still have, and enforce, a policy that's similarly horrible to what Southwest was originally doing.)
"Fat privilege" is the ability to easily unlock other adults' inner children—if we accidentally brush against someone, and especially if our skin actually touches them when this happens, some people will actually react as if we have cooties and have therefore just infected them, just like we used to on the playground when we were kids.
Yes, fat people really are just swimming in privilege.