The same thing should apply to STDs. If someone chooses to be promiscuous, it's their choice and we should not be paying for their medical care and abortions. If someone chooses to take drugs, there is no procedural difference between ingesting drugs and ingesting fat food. They should pay for their own medical care or die.
Their choice, their cost.
Why not also people who sky-dive, rock-climb, jog, drive fast, lay on the couch and don't exercise, decline to take prescriptions, don't sleep enough, eat "too much" red meat, work "too many" hours, aren't married, don't have kids? Each of those also have physical and mental health consequences too, so we shouldn't have to pay for their healthcare either, right?
See where that kind of thinking can lead? "Oh, no," you say. "That will never happen!"
Really? Once upon a time we never thought we'd be having this conversation about fat people either...but here we are.