It's well known that eating less "caloric restriction" slows down your metabolim and thus extends lifespan in mice. This would be my default hypothesis.

Half of the article discusses the whole concept of "biological age", and that discussion describes how that term may not be as refined and specific a scientific idea as a layperson might assume. That part of the article might be served by the title, "Weight loss drugs may help scientists to assess potential surrogates for biological age."

How can they separate this from the effects of losing weight?

...convienent.