There was a law suit by a soft drink company saying they were singled out when other food manufacturers with equally vacuous food products were not taxed. (The court did say that the legislature did have sufficient reason to be specifically concerned about soft drink manufacturers. Courts generally defer to the legislature making that kind of classification, and even in making a statute constitutional or unconstitutional.
But from a participatory democracy point of view, we simply need to have sortition juries compare the products and allocate taxes based upon their perception of badness. No categories are needed, we don't have judges making these value judgments that this item is "junk food" and this item isn't. We just present the information on the products to the sortition jury. Hopefully, the jury can reach a consensus on the tax rate for each product. If not, each juror votes on what tax each product should pay. The average or median of the votes is the is the tax rate.