The Y chromosome is theorized to facilitate evolution of sexual dimorphism by accumulating sexually antagonistic loci, but empirical support is scarce. Due to the lack of recombination, Y chromosomes are prone to degenerative processes, which poses a constraint on their adaptive potential. Yet, in the seed beetle, Callosobruchus maculatus segregating Y linked variation affects male body size and thereby sexual size dimorphism (SSD). Here, we assemble C. maculatus sex chromosome sequences and identify molecular differences associated with Y-linked SSD variation. The assembled Y chromosome is largely euchromatic and contains over 400 genes, many of which are ampliconic with a mixed autosomal and X chromosome ancestry. Functional annotation suggests that the Y chromosome plays important roles in males beyond primary reproductive functions. Crucially, we find that, besides an autosomal copy of the gene target of rapamycin (TOR), males carry an additional TOR copy on the Y chromosome. TOR is a conserved regulator of growth across taxa, and our results suggest that a Y-linked TOR provides a male specific opportunity to alter body size. A comparison of Y haplotypes associated with male size difference uncovers a copy number variation for TOR, where the haplotype associated with decreased male size, and thereby increased sexual dimorphism, has two additional TOR copies. This suggests that sexual conflict over growth has been mitigated by autosome to Y translocation of TOR followed by gene duplications. Our results reveal that despite of suppressed recombination, the Y chromosome can harbor adaptive potential as a male-limited supergene.