No more than they do against smokers, alcoholics, or drug addicts.
Just hear me out.
We like to pretend that people can't get addicted to food, but have you ever talked to one of the people riding in the scooters at a grocery store? As a cashier I have to interact with them all the time, and as both a smoker and a recovered drug addict, I know one or two things about what addiction is like... and they have an addiction. There are a sizable number of people in our society who are so overweight that they can no longer walk the distance of a grocery store.
Let me repeat that... THERE ARE A SIZABLE NUMBER OF PEOPLE IN OUR SOCIETY WHO ARE SO OVERWEIGHT THAT THEY CAN NO LONGER WALK THE DISTANCE OF A GROCERY STORE! They're miserable, they're feeling the constant pains which are a symptom of obesity, they can't get any of the feel good chemicals which are a natural result of exercise, they smell horrendous because there are parts of their body which they can not reach to clean. That's right, smokers like myself aren't the only ones who smell unpleasant. If you've ever had the misfortune of having to drive one of those grocery store scooters, then you know first hand that the odor on these people is so thick that it is permanently left on anything they sit on. There is a palpable smell on those scooters.
NO ONE would choose to live like that. EVER. E. V. E. R. And yet the people in those scooters inevitably come by with the same unhealthy foods which will only make their conditions worse. What tiny amount of happiness can they hope to gain from a box of Cheez-its or a two liter of soda? They are chasing a high. Not only that, anyone who's ever tried dieting knows how unpleasant that can make you feel, but imagine if you were as out of shape as these people are. Those are called withdrawal symptoms.
So having made my case that these people are food addicts, I'll reiterate my point. If it's okay to discriminate against smokers, alcoholics, or drug addicts (and for the most part our society has deemed that it it is) then it's no worse to discriminate against the obese. The results of their addiction can make them unpleasant to be around, both in terms of attitude (I have yet to meet a single person in one of those scooters who was chipper and seemed filled with the joy of life) and to the extend that their odor and unkempt appearance is genuinely unpleasant. I hate to put it like that, but it's hard to see someone in one of those scooters and not be disturbed by the reminder they bring, of a slow, painful, self-imposed death.
Having said all of that, I think that it SHOULD be inappropriate to discriminate against any addict. From a sociological perspective, the reason we discriminate against addicts is that they have broken a societal more, and the discrimination is the punishment they get for breaking those mores. It's meant to be a deterrent... "don't live like them, or people will treat you that way too." While it actually is a good idea to try and deter people from succumbing to addiction (trust me, I wish I'd been better deterred from smoking), the fact of the matter is that treating people who suffer addiction as outcasts only makes the situation worse.
When someone's rude to me because I smoke I don't think to myself "well maybe it's time to quit." I was thinking that before, but when people are assholes our natural human response is to dig our heels in. I don't say "well, now I really should quit," I say "fuck you! I smoke because I want to smoke, and there's nothing you can do to stop me!" It's a lie that we tell ourselves when someone tries to make our lives worse because of our flaws, we don't give in, we start justifying our own bad behavior. These women, it sounds to me, are doing the exact same thing that I do. They're not going, "well, maybe you have a point... perhaps it's time I lose some weight." They're saying "fuck you! I'm obese, and I'm proud!" They are making a positive out of the unpleasant results of their addiction... it's a coping mechanism. And while it helps their hurt feelings, it won't help them recover. To indulge that kind of justification is to be an enabler.
If you want to help people with addictions, people like me, or these women, you don't discriminate, and you don't tell us that we're lesser human beings. We don't need a good talking to, we need support and help. The obesity epidemic won't end just because we identified it and pointed out all the horrible things that people who suffer a food addiction go through. It'll end when we start to offer people a better alternative, when they have help pushing through the difficult process of quitting, and are certain that they can do it because they've got that reassurance every step of the way.