Greg Mankiw proposed a height tax as a bit of a reductio on the efficient tax literature. You can't adjust your height; height predicts income. So tax height and incentives around income remain clean. Ta-dah!
Work in the BMJ suggests that the height-income link is causal from height to income and works through genes - but mostly for men. A standard deviation (6.3 cm) increase in genetically predicted male height is associated with a £1580 increase in income. Obesity matters too, but for women. A standard deviation increase in genetically predicted BMI reduced women's household income by £2940.
I still await confirmation of the Python hypothesis that taller archaeologists are better archaeologists.
More seriously, though: some of the fat tax arguments hinge on that the link runs from obesity to income through health. Otherwise, they couldn't run a counterfactual that earnings but for obesity would be the same. That underlies the productivity costs of obesity argument. Where predicted obesity from genetic markers drives income, the argument for fat taxes to improve productivity get a bit fraught.