I don't think that study (coincidentally from the maker's of semaglutide!) is answering quite the same question I'm asking, since it only looked at people aged 20-65 that were still alive without considering the difference in average lifespan.
If an obese person's healthcare costs an extra $2,000 annually for each of the age years covered in the study, that's $90,000 over their lifetime (ignoring inflation/time value of money to keep the numbers simple). But older people tend to have disproportionately higher healthcare costs.
To be kinda crass: If hypothetically obese people die at the age of 70 instead of 75, those 5 years of health care they don't need might have cost more than $90,000. Just a few ER or ICU visits can exceed that $90,000 amount, and the gap gets even starker if you take into account things like long term care and assisted living.
Another way to look at it, even staying within the 20-65 age group, is as a form of survivorship bias (or maybe there's a better term? Seems kinda bayesian but my stats days are well behind me)
For an extreme example, pretend that some adults take up the hobby of BASE jumping, and I have a study showing that their healthcare costs $10,000 per year, vs only $5,000/yr for non-base jumpers. A non-basejumping adult only needs $225k of healthcare before they become a senior citizen, but a basejumper needs $450k! So basejumping increases overall costs in the healthcare system, right?
But wait! BASE jumping is a dangerous activity (hence the medical bills), and many BASE jumpers die young. Let's say that every year 5% of BASE jumpers have fatal accidents, which means that the average base jumper dies around the age of 33. A BASE jumper who only needs medical care for 13 years doesn't cost the full $450k, they would only use $130k of healthcare. Which actually makes their lifetime medical bills much cheaper than that of a non-jumper!