Stone does weather too. It either needs uninterrupted dry climate (not really possible for millions of years) or being placed inside a stable geological formation (we don't usually build that way).
We are talking about actual bones in living animals though, and those surely fossilize (preserve over eons) much more rarely than many civilizational artifacts.
> those surely fossilize (preserve over eons) much more rarely than many civilizational artifacts
I don't think they would fossilise. It's a process specific to the porosity of organic tissue. They might be preserved, but the Cambridge paper explains why it’s unlikely they would last for a hundred millennia or more.