It's not proposed as a revenue raiser, it's intended as a public health measure.

The idea is that people buy less sugary drinks and have better dental health.

Your concerns raise a valid point, though, that revenue raised (and $1.4B isn't nothing) should be directly funneled into new programmes that benefit the working class. The study suggests that the money go into dental and other health services, but I've also seen proposals for using the revenue to cross-subsidise fresh food.

Either way, the working class could see a net benefit to their bottom line from government subsidies (which benefit from efficiencies of scale) and because they'll have less need of dental and other health services if they reduce their sugar intake.