I’m down for taxing fat people to neutralize the externalities they create but I don’t think selling unhealthy food has negative externalities. Eating too much does so sure tax the eater. There is zero external downside to a healthy person eating a moderate amount of unhealthy food.
Taxation as a behavioral incentive is typically applied os a sales tax. So in practice this is a consumption tax, not a production tax.
The externalities in this case are caused by the producer/promoter, as an externalized health risk. What you are probably refering to is the secondary effect of aggregate increased healthcare cost.
There’s no external health risk though. I reject the idea that people don’t realize unhealthy food is unhealthy, they just dont care enough to stop eating it. The health risk is completely internalized.