Well, okay. First, let's take a look at the law itself:
Any food establishment to which this section applies shall not be allowed to serve food to any person who is obese, based on criteria prescribed by the State Department of Health after consultation with the Mississippi Council on Obesity Prevention and ManagementThe analogy to alcohol starts immediately. How do you know someone is obese? Well, how do you know someone is drunk? The bartender knows based on a series of signs, including slurred words, loose body movements, uncoordination, loudness, etc. It would appear that they'd like this same vague "knowing" to apply to judging someone's weight - except, weight isn't that easy to determine. Looking at me, you wouldn't guess I weigh what I do (it even surprises my doctor), and I certainly would never be a candidate for withholding a meal in a restaurant...based on my looks. But at one point in the recent past, my BMI certainly was in the category that qualified for obese.
So then, what - wait staff are supposed to take their average best guess on someone's weight, BMI, fat versus muscle mass, and etc? Can we say lawsuits based on discrimination? (I thought we might.)
The problem here, and the way that as much as it might be nice to draw parallels between drunkenness and obesity, is that drunkenness does typically have the same basic set of signs no matter who you are. It doesn't matter how tall or short you are, your genetic history, your medical history - nothing. Being drunk is the same thing, and therefore relatively easy to determine (and especially the ones who should be completely cut off).
Being obese is not the same thing. Your rate of obesity does vary on size, on body type, your genetic history, your medical history. Everything. Obesity is a matter of your physical body and its relationship to your environment and your culture, and therefore not at all easy to determine (and certainly not by inexperienced wait staff).
Finally, and perhaps the clearest distinction, and hole in the argument being made, is that if you don't cut off someone who's drunk, their potential for death goes up that night - as does their potential to kill someone else. Even if someone who's obese eats themselves to death, they're not going to kill another person as they do it. They're not going kill another person with them or through their mistaken judgment. Time is on the obese person's side, it's not on the side of the drunk person trying to drive.
Perhaps it's a rather strict utilitarian view, but it does seem to me that if you choose not to cut off someone who's drunk, and they go on to hurt or kill another person, you are at least to some degree at fault for not trying to stop the drinker. But the chances of someone who's obese not being cut off from their food and then going out to hurt or kill another person seems... unlikely, to say the least. This is not to say there are not consequences from being obese, but they are a different set of consequences, and primarily affect the obese individual rather than a person who's suffering at the hands of a drunk driver.