The solution is to tax added sugar (including for sub-ingredients) per gram, and a flat tax for any food containing artificial sweeteners. 1c per gram of sugar, or 20% for anything containing artificial sweeteners seems reasonable.
A sugar tax would mostly impact the people who have the least choice in what they buy, due to poverty and/or the availability of healthier foods. (See: food deserts)
Better to work on the affordability and availability of healthy food than try to penalize people for buying stuff that's cheap and ubiquitous. If you want to apply sticks, apply them to large retailers like Wal-mart and Target instead of to individuals.
If 1kg of Oreos (41% sugar) costs $3.60 instead of $3.19, people will spend the same but just consume 11% less, or manufacturers will recreate the recipe to have less sugar. Both of those outcomes are good.
The money collected can be used to subsidise community kitchens, or raw fruit and vegetables.
To me, the solution has to be trying to get people to eat healthier things via education. I mean, the "incentive" is feeling good, looking good, being fitter and more capable.
One thing I've found particularly motivating as a parent is that a good diet is a huge competitive advantage for my children. We live on a farm, so we've always got great, healthful things to eat, and since we harvest ingredients and not factory-processed stuff, they're always cooking--it's not just their health now, but their ability to be healthy adults.
https://academic.oup.com/jn/article/146/9/1722/4630474
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5855172/
I wish there were more giant community kitchens in the West, as are commonly seen across Asia. This is one extreme example: https://www.youtube.com/watch?v=TT-N5wl0l-s
And at a smaller scale in Melbourne, Australia: https://youtu.be/dG8hH8zE7ZI?t=169