From atoms to molecules
So far we have been counting atoms. But most things in nature do not exist as atoms.
Most elements are reactive, so their atoms do not exist as free atoms. They occur naturally as molecules, formed when two or several of their atoms join together.
Atoms of the same kind
When atoms of one element join, the result is a molecule of that element — oxygen as O2, nitrogen as N2, hydrogen as H2.
Atoms of different kinds
Compounds consist of molecules formed by the combination of atoms that differ from one another — water as H2O, carbon dioxide as CO2.
So the question changes too
Instead of asking what one atom weighs, we now ask what one molecule weighs. The way to answer it is unchanged — compare against the same standard — but it is given a name of its own.
The standard does not change
Even for a molecule, the denominator is the same thing it always was: 1/12 of the mass of a 12C atom. That is what lets relative atomic masses and relative molecular masses be compared with one another — both are measured against the same standard.