Hypertrophied sexually dimorphic eye stalks have evolved independently in several families of Diptera, with the eyespan of males exceeding their total body length in some species. These structures function in intermale contests for territories and in mate attraction, the classical mechanisms of sexual selection. In the family Diopsidae, species with extremely exaggerated eye stalks and marked sexual dimorphism in relative eyespan also usually have strongly female-biased sex ratios in nature caused by X-linked meiotic drive, whereas species with relatively small eye stalks have little or no sexual dimorphism, often lack meiotic drive and have even sex ratios. We investigate the possible connection between sexual selection and sex-ratio meiotic drive by analysing a three-locus model for the evolution of female choice for a male character associated with meiotic drive. Both meiotic drive and the male character are X-linked and the female preference is autosomal. Our model shows that suppressed recombination between meiotic drive and the male character, e.g. by inversion of the X chromosome, is necessary for sex-ratio selection to promote the origin of female mating preferences and exaggerated secondary sexual characters. With complete suppression of recombination, sexual selection reduces the frequency of meiotic drive, and may eliminate it. Very rare recombination, gene conversion or mutation, at rates characteristic of chromosome inversions in Drosophila, restores the meiotic drive polymorphism to its original equilibrium. Sex-ratio meiotic drive may thus act as a catalyst accelerating the origin of female mating preference and exaggerated male traits.