As we see here, obesity and very low body weight are both associated with worse mental health outcomes. Merely being overweight, interestingly, seems to be associated with better mental health outcomes. This tracts, being overweight isn't necessarily associated with the kinds of unhealthy or dangerous behavior that obesity is - that's just a problem of quantity rather than quality.
To clarify, I didn't say to ban the ingredient itself, just foods with added sugars i.e. sugar-sweetened beverages, sugary snacks and junk food, sugary breakfast cereals, etc. We're talking about this in context of the tax, which doesn't ban raw bags of sugar.
If someone wants a teaspoon of sugar in their coffee at home then whatever, that's not the source of the public health crisis. The problem is from convenience and processed foods. We could solve the problem. We won't.