Diameter certainly has an approximate relationship to mass. Approximate for the reason you describe, the variation of string structure altering the density of the string structure.I still disagree that diameter has anything to do with mass or tension,
For smaller gauges, the core wire tends to have a gauge that is larger relative to the full gauge, a.025 may have a .012 core while a .130 has a .020 core (rough guesses). The core wire is solid metal while the wrap wire layers have air gaps.
There are also differences in number of wrap wire layers.
The assumption of constant string structure density allows some rough and useful rules to be used, which work fairly well if checked against a tension chart based on actual measured masses.
For example, a very useful rough rule is:
"For 2 strings of equal length and tension, the ratio of gauges will be roughly equal to the ratio of frequencies"
Since the frequency ratio of a fourth interval is (very close to) 4/3, the ratio of adjacent string gauges will be roughly 4/3 if equal tension is desired.
The rough rule results in the sequence .045 .060 .080 .107 which is actually a D'Addario balanced tension set. Checking the stated tensions (mass based) they are fairly equal.