Soda taxes don't do much to affect obesity. A new paper by Fletcher et al in Health Economics looks at effects of American soda taxes across U.S. states. While 'soda taxes' aren't common, differential sales taxes on soda aren't uncommon; soda is often exempted from generalised food exemptions from state-level sales taxes. Consequently, soda can have an effective tax rate of up to 12% more than other foods and non-alcoholic beverages, though the average was much lower.
They find that sales taxes have no statistically significant relationship to soda calorie intake and may increase consumption of calories from non-soda beverages. In one specification, they find that a one percentage point increase in the soda tax increases total daily caloric intake by 27.7 calories; I rather suspect that they're here picking up an endogeneity problem: governments will implement soda taxes when obesity is rising.
Supporters of soda taxes have suggested that tax hikes in the range experienced in the US will understate the potential effects of a much larger tax hike: if effects are non-linear, this is entirely possible. But Fletcher et al find zero evidence of non-linearities in tax effects within the range of US taxes. If there were some non-linearity, we'd expect there to be at least a little action in the quadratics and high-order polynomials; the linear specification fits best. But we can't rule out non-linearities that only kick in well outside of sample.
They'd previously found strong evidence of substitution effects among children and adolescents: taxes on soft drinks reduced soda consumption but induced an entirely offsetting increase in calories from other non-soda drinks. And recall that Klick et al found that relative prices of healthy and unhealthy foods didn't affect obesity either.
See also Paul Bedard at the Washington Examiner and Chris Snowdon.