Why not just target the output, rather than some random subset of inputs? We could tax obesity if we wanted to. Or if we want to seem less punitive, we could award tax credits to obese people who lose weight. A tax directly pegged to reduced obesity would certainly be a much more efficient way to achieve the stated policy goal of reducing obesity.
Of course, “fat taxes,” even when framed as weight-loss tax credits, seem pretty loathsome. Why is . . . unclear.