In a cool experiment, it was demonstrated that taxing unhealthy food is more effective at encouraging healthy shopping than subsidizing healthy food.
Of course in the real world, we basically do what could be inferred from this experiment as being the worst of all worlds. That is, we not only do not tax unhealthy food, but we actually make it cheaper via subsidies. Because meat, dairy, corn, etc get more government subsidies than fruits and vegetables, we are making unhealthy food cheaper relative to healthy choices.
The logic of the cigarette tax is that smoking costs society. The smoker is someday going to be treated for smoking-related diseases from the medicare fund, and that is going to be an enormous financial burden on society. If smokers are going to cost more, they should pay more. The exact same argument applies to taxing unhealthy food.
Support of food taxes will beget the label of a big-government socialist or a paternalist. Case in point, this commercial that is against the soft drink tax. My rebuttal is simple. If your family is so scrapped for cash that they cannot afford a soft drink tax, don't buy soft drinks!