Molecular mechanism [reduced female variance] is most likely barr-body mediated mosaicism in female somatic cells. I've seen some data in the past that points to this.

In other words, the random inactivation of one of the X chromosomes in each cell means that females experience "averaging".

Males have only one X chromosome, and do not experience this averaging.

As the X chromosome has lots of transcription factors (as one might expect), the simple averaging of dosage levels and so on between cells via random X inactivation is likely to reduce phenotypic variance for most characteristics.