A tax on sugar is both a sin tax and a Pigouvian tax. IMO the real reason for its introduction was the sin tax angle, but it's Pigouvian tax principles is what makes it a "good" tax.
https://theconversation.com/rejection-of-sugar-tax-is-based-...
Levying a tax targeted at the poor does not "benefit" them.
Nobody is disputing sugar taxes are regressive, they’re disputing that’s actually a bad thing.
Research indicates smoking among Australian teenagers declined by about 65-70% in the 15 years to 2014.
[1] http://www.tobaccoinaustralia.org.au/chapter-1-prevalence/1-...
Debatable. Here is one study[0] that claims that while it has minimal effect on people who already are heavy smokers, it does have an effect on reducing the consumption among the young.
Semi-related: https://www.theatlantic.com/business/archive/2015/03/finland...
Soda is basically poison. The producers would be driven out of business in any rational economy where they were not shielded from product liability law suits.
A free market requires a free and just legal system. In the US every single producer of toxic and deadly products has their own specially granted immunity from product liability, either by judicial custom or legislation.