I'm guessing that if you weighed all our passengers with all their luggage, women would still be lighter on average. Shoes, make-up and underwear weigh a lot less than human flesh, and men are still bigger than women on average.
There is some validity to the idea of charging people for carry on luggage. Didn't Spirit do this a few years ago? I don't know if they still do it. I remember the idea was met with a lot of criticism, but isn't the overhead space a desirable product? No one wants to check luggage, but they all want the overheads, so why aren't we charging for it?