An awful lot of people are obese in the UK, and even more are overweight. I doubt many of these at all are so unhealthy that they actually require NHS help, (I doubt anyone who's only overweight ever has weight related issues, it tends to be morbidly obese people, which is far different from 'fat'), so I doubt the NHS argument is valid, also many people go to the NHS because of smoking and alcohol, and we don't stigmatise them (especially people who drink and party, yet I see people go to A&E for getting too drunk and doing something stupid, but that's just cool apparently).
So onto the other point, not all fat people just started one day to eat loads, some of them (especially kids when you see it) were raised by overweight people themselves and just developed bad eating habits. Of course this should be dealt with and people should try to have healthier diets, but making young people (or anybody) feel horrible for how they choose to enjoy food will just make them feel like utter crap, and we shouldn't scare people into doing what's best for them because it seems unfair to make people feel terrible about themselves.
It has no bearing on you whether some random person is fat or not, so why fuss at them about it? If they want to eat themselves into unhealthiness, then making them feel like crap probably won't help, it'll just make them sad which, guess what!, will make them eat more! If it's someone you know/care about, the situation is different and should be handled delicately, but this question wasn't about that.
If you really think fat people don't know the health risks then that's far from true. Many fat people aren't nearly dying anyway, and the last think they want is everyone to just think of them for their weight, and fussing at them over and over to lose weight will just make them feel worse. If they go on a diet give them support, tell them how great they're doing, and they may keep it up longer, but making them feel bad in the first place won't make them feel any better and often won't drive them to lose weight.
Argh I could rant more but I swear I've seen this topic so many times, except usually worded in a more mean way than OP, so yeah..