Some decade ago, a bike science group did a test. They put a black water bottle on the test bike, sometimes it was filled with lead and sometimes it was filled with air. The rider was not permitted to lift the bike or bottle. At the end of the tests, not much difference between air and lead. The only difference was the expected hill climbing horsepower to weight factor.
When weight matters, it's total weight not wheel weight, bike weight, or rider weight. (bikes don't accelerate fast enough for rim weight to matter)