In this case the fat tax is intended to tackle the "epidemic" of obesity. But it is not a tax on fat people, but on selected foods deemed to contribute to obesity. Why? I'm pretty sure that it is possible for a thin person to eat doughnuts, and for an obese frame to be maintained with sufficient quantities of muesli and semi skimmed milk. More specifically the argument is precisely that fattening foods are a problem, because it is a problem that people are fat. So a tax on fat people would surely be much more to the point. Yes, there are practical difficulties with a tax on fat people. All that weighing. But let's park that for now and just consider the principle.
The problem is that a tax on fat people would be grossly unfair, offensive and discriminatory. Thus the attempt to levy an extra tax on fat people by proxy, in the hope that we thereby don't notice that the policy is grossly unfair, offensive and discriminatory.
I've had some feedback on this argument from @IanEiloart, @beccaet and @MsNoeticat, which I will address here without attributing particular views to any one person. Thanks for your comments, by the way.
First is the question of whether a fat tax would produce a social benefit by incentivising food manufacturers to change their recipes in a lower fat direction, i.e. to make their regular products more like "diet" products. You know diet coke, diet yoghurt, diet ready meals. All the bulk of the regular product with little of the flavour. There's a reason I don't buy diet products: they are horrid. Making food in general more horrid is not something I would count as a social benefit. Just as starving sailors lost at sea would fill their bellies with sawdust to quell the hunger pangs, the modern body-image conscious person is supposed to fill their belly with a modern food-sciencey equivalent such as cellulose (which may be made from sawdust in fact).
Second is the point that pushing diets in the right direction will benefit everybody. Will it really? Will it benefit people who are underweight? How many borderline anorexics will be pushed over the borderline because they are eating food with more cellulose and less food in it? The problem here is that we are looking at the average person - who may be overweight - and imposing a food policy for everybody, as if everybody was the same as that average person. Many people eat too little fat or too little cholesterol, or too little proper food of any kind. Should they be sacrificed on the altar of the average? Top down, one-size-fits-all policies fit very few.
Finally the suggestion that revenue from a fat tax could be help people who are struggling with weight issues. This is true. And it is fair to say that weight is a very big problem for some people, causing a great deal of distress and poor health outcomes. I do think a fat tax would have to be very high indeed in order to help everybody in this kind of need, which raises the question of why isn't this kind of health support more of a priority anyway? Why should it rely on a hypothecated tax? We don't hypothecate tobacco and alcohol taxes to particular health interventions, and nor should we.
And I would say that a large part of the distress surrounding weight issues is a result of social pressures to conform to a perceived weight ideal. Now what is the fat tax, but another kind of pressure to conform to that same perceived ideal? On the one hand we are campaigning against unrealistic body images in the media; do we really want to turn round and try to impose unrealistic bodies on people through the tax system?
Update: see also freakonomics.