That's the topic of Taxing Sugar Sweetened Beverages to Lower Childhood Obesity by Sarah Wetter and James Hodge. Here is the abstract:
Consumption of sugar-sweetened beverages (SSBs) contributes to multiple health problems including obesity, diabetes, and tooth decay, especially among children. Excise taxation has been proven efficacious in changing purchasing behaviors related to tobacco use with resulting improvements in public health outcomes. Similar taxes applied to SSBs are starting to take hold internationally and domestically. SSB taxes have been proposed in over 30 U.S. jurisdictions since 2009, but only Berkeley (CA) has passed and implemented one to date. Given empirical evidence of their effectiveness, governments should consider implementation of SSB excise taxes based on uniform definitions of SSBs and other factors.