Earlier quoted context omitted.
Healthcare systems can scale up to meet the extra demand, and obese people can be asked to pay more for their healthcare. That doesn't apply for phone driving/drunk driving/etc because you can't charge people more based on the risk that someone else might hit them.
We can’t staff for the current level of demand of our healthcare systems, how would we “scale up”? Additionally, this article is about the UK where healthcare is paid through taxes. Are you suggesting the overweight pay higher taxes?
The UK uses a nationalized essentially communist form of healthcare provisioning and then gives it away for free to anyone who turns up, legally or otherwise, so they should expect constant shortages. Nobody else uses that system for a reason. However the UK is unwilling to change, so it's not something you can generalize from. There are other places in the world where healthcare systems do scale up just fine and supply keeps up, because they provision differently.
BTW the UK government does impose all sorts of sin taxes on people already, and provides benefits based on health assessments, so tying tax levels to the outcome of similar health assessments isn't a big leap. But yes in reality it'll be countries with more flexible insurance systems that can calibrate things that way.