Social reasons it would never work. I hate to mention anything race related online but simple truth is America has complicated history and African Americans are 30% more likely to be obese than White Americans and also earn approximately 60% of income that whites earn. A fat tax, especially one that properly allocated the cost burden to the individual, would erode race relations.
Is that controlled for income / poverty levels?
It doesn't matter as the cited numbers will be cherry picked.
fwiw the “tax” in Japan is not paid by the individual, and generally taxing the behavior via e.g sugar taxes rather than the outcome has worked better without much public outcry after the fact
Not sure that would play the same in US though.
Black population in the US is still concentrated in neighborhoods formed by overt racism and segregation and same neighborhoods tend to be food desert where no healthy or even fresh options exists. Even if we taxed just the bad food, the lack of options and mobility that higher income might provide, basically means it’s something that would be seen as targeted. Not to mention, people will draw the most racist perception no matter how carefully you crafted the tax because race relations are always unfortunately weak and these correlations are being forced/drawn.