This short piece in the British Medical Journal, focusing on a fatty-food tax in Denmark, says that the evidence is equivocal. One problem is that consumers may respond to a fatty-food tax by substituting cheaper (but still fatty) foods for more expensive fatty foods. Another problem, believe it or not, is that consumers may buy their fatty foods in other countries that don't impose a fatty-food tax (just as consumers might do the same in the U.S. if one state has a fatty-food tax but a neighboring state does not). But there's some evidence that consumers will eat healthier foods when fatty foods are taxed. The authors conclude that more study is needed.
We've posted earlier on efforts in the U.S. to impose taxes on sugary sodas.