This has consistently proved false.
Being 'underweight' is associated with significant excess death; being 'overweight' is associated with a lower death rate than 'normal' BMI:
e.g. https://jamanetwork.com/journals/jama/article-abstract/20073... (many other sources are available)
This is nonsense. In many medical deaths such as cancer (and especially since euthanasia isn't available) the person dies by slowly withering away. One of the first things that happens is that they become skinny and frail. That doesn't associate underweightedness with mortality. It intentionally draws a false correlation.
[Edited to add: this article explicitly considers the link to cancer, and rejects it, https://bmcpublichealth.biomedcentral.com/articles/10.1186/1... ]
However, it doesn't explain why being 'overweight' BMI consistently proves to be protective against death, despite it being so stigmatised that it affects quality of medical care.
I don't see how the "protective of death" conclusion is able to be maintained when it was determined by comparing the mortality of overweight people to frail and dying old people and cancer patients. The reality is that it's the opposite. It's well known that being overweight damages the organs and makes a person more susceptible to dozens of diseases.
Also, being "overweight" could be for a variety of reasons, including excess muscle. I'd be interested to see mortality correlated with % body fat.
> Excess Deaths Associated With [...] Overweight
Results:
> Overweight was not associated with excess mortality (−86 094 deaths; 95% CI, −161 223 to −10 966).
"Are excess deaths associated with being overweight?" (The result is: no - or actually yes, but negatively).