Unfortunately, your argument runs into an opposite extreme. Yes, freedom is important, but it's not the only thing that's important. There is different, but similarly strong argument that society should preserve life.
Freedom dictates that people should be allowed to do what they want, even if it causes self-harm. Life preservation dictates that we should do whatever it takes to preserve life. Both of these values are are pretty fundamental, baked into most religions and political philosophies. Sometimes however, as in the case you point out, these two values butt against each other.
The answer is not to choose one or the other, but to properly balance them.
It’s absolutely not an extreme view. We already do this for food, for example, which is also required to support life. Being hungry does not entitle you to steal from a supermarket, under our system.
Forcing hospitals to treat anyone regardless of ability to pay is really just forcing an unfair tax onto everyone else who happens to use that hospital in the form of increased prices. That’s not a reasonable system.
You get both individual freedom and remove the harm to others from obesity if you stop forcing service providers to work for free.
The only reason that people who choose to become obese are a drain on others is because there is currently a mechanism for them to force others to absorb the cost of their resulting health care.
Make it so that people have to pay for healthcare for themselves either out of pocket or via insurance instead of forcing hospitals to serve all comers (like any other service that is provided to people), and suddenly you get the best of both worlds: everyone gets to eat what they want, smoke what they want, inject what they want, and nobody else is forced to pay for the poor decisions of anyone else. Everybody wins.