There is a some discussion of a soft drink tax. The argument is a bit different from a pollution tax, in that a pollution tax addresses a negative externality, whereas a soft drink tax is more like a sin tax--taxing people who do things to themselves that we don't like. There isn't much of an economic justification for this (unless overweight people impose a tax externality on others due to using state-funded health care for their expensive health care--only they don't seem to have higher lifetime health expenses because they die earlier), but even if there were, it seems to me there is a significant problem: substitution. There are plenty of ways to satisfy a sugary craving for calories, aside from a soft drink, and although they may not be perfect substitutes, I doubt a soft drink tax would be sufficient to make much of a dent in obesity.
A general calorie tax might work, although that, too has problems--it would be very costly for small-scale food producers that otherwise don't have to provide nutrition information, as they'd have to calculate the calories in their food in order to figure out the tax (and exempting them from the tax seems to be to be unfair--it penalizes large producers for being successful). Such a tax would also make it more difficult for the poor to afford food of all kinds (currently the poor are more likely to consume unhealthy food and suffer obesity). We would have to create an algorithm for determining what food is healthy or unhealthy, and therefore how much to tax it, rather than a simple calorie or soft drink tax--but that is even more elaborate and difficult to get right, and even worse, it's going to be subject to lobbying that could give us even less healthy relative food prices.
A safer start would be to eliminate agricultural subsidies and protective tariffs and see what happens. I suspect that so long as America remains relatively rural and suburban (compared to Europe), obesity will remain a problem.