Wouldn't this cause insurers to have to raise their premiums for everyone substantially?
This is a big claim to assert without evidence. If it was the case then insurers would already be adding the drugs to their formularies.
There is undoubtedly a cost associated with obesity but you are suggesting that simply being overweight doubles the average cost of care[1], a figure that already includes overweight and obese people (which are of course a huge population in the US).
A quick Google search turned up a report[2] that suggests that
> This estimated public cost equates to an average marginal cost of $175 per year per adult for a one unit change in BMI for each adult in the U.S. population.
So, even for the extreme case of a very obese person that has a very successful treatment and goes from 40 BMI to 25 BMI, you are only saving a hypothetical $2,625 per year (perhaps an underestimate due to inflation and the age of the paper).
Therefore it would appear that unless insurers strike a deal with the drug companies (lower the price, make it up in volume), such a law would dramatically increase insurance premiums. A better compromise would be a law which requires insurance companies to offer co-insurance on these drugs up to the expected savings.
[1] https://www.pgpf.org/blog/2023/01/why-are-americans-paying-m....
[2] https://vinecon.ucdavis.edu/wp-content/uploads/2019/04/cwe12...
American healthcare system has perverse incentivizes. Most unhealthy groups are generally least likely to be privately insured, so insurers are incentivized to prioritize health issues affecting working-age adults, while neglecting those which will be someone's else concern in future.