I never mentioned the impact the taxes have on the poor, it's not really a huge concern for me.
If the government wants to help the poor they can do so through extended, strong, social security nets, good education policy, and a strong progressive tax system. If the poor are doing something that is harmful to themselves then making them stop through tweaking the system properly will not hurt them in the long run, it will help them.
I am unconvinced that the health consequences of consuming so many high fructose drinks are not an externality.
Externalities are harms done to others by an actor. When a person drinks sugary drinks they are deciding to perform some action to themselves, it is not the case of the sugary drink companies producing things that harm others who have no control over the situation. People can, even if addicted to a substance, choose to stop using sugary drinks.
You can't chose to or not to be effected by carbon emissions, you can choose to drink or not drink sugary drinks. The government should focus on ensuring people have that choice through information campaigns (informative ones, not propaganda ones).
lung cancer through second hand smoke is a negative externality of cigarettes. Lung cancer in smokers is not. In this way the statement would be that smokers, who choose to smoke near other people should be responsible for the damages they do to them. In fact, they are, through higher insurance payments and high cigarette taxes.
We can solve obesity without resulting to excessive taxes, but through setting up the system to function properly in the first place.