Whenever an activity exerts a negative externality on others, you want to tax it. For example, sin taxes are in place or are proposed for smoking, eating junk food or drinking soda. The reasoning is that these activities are bad for health, and thus end up costing society, even when there is no socialized health care. The fact that these unhealthy people tend to live shorter only partly offsets the direct effect of the externality.
Catarina Goulão and Agustín Pérez-Barahona explain that there is another good reason to tax unhealthy food: unhealthy eating habits are transmitted from a generation to the next even when there is no genetic reason for this to happen. This can also within a group of socially interacting people, which gives obesity or smoking the characteristics of an epidemic. To break this vicious circle of learning, the price mechanism has to come to the rescue. So let's impose more or new sin taxes. We could use the revenue, apparently.