Denmark tried it and has now abandoned it as unworkable.
Denmark’s tax was just high enough to become a nuisance for manufacturers — and to act as an incentive for cross-border cookie runs — without making a significant impact on how people actually eat.
A May British Medical Journal study found that ”fat taxes” would have to increase the price of unhealthy food by as much as 20 percent in order to cut consumption by enough to reduce obesity, and they should be paired with subsidies on fruits and vegetables so consumers don’t swap out one unhealthy habit for another.
We're going to need better ideas, because the problem addressed by the fat tax has not vanished with this one failed remedy.