Atomic weight of two hydrogen atoms = 2
Atomic weight of one oxygen atom = 16
Atomic weight of H2O (water vapor) = 18
Atomic weight of an oxygen molecule = 32
Atomic weight of a nitrogen molecule = 28
Equivalent atomic weight of air
(80% N2, 20% O2) = 28.8
18 is much less than 28.8
QED
edit: Mea culpa, kindly substitute "Mass" for "weight" in above text.