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Sexual dimorphism in complex traits is suspected to be in part due to widespread gene-by-sex interactions (GxSex), but empirical evidence has been elusive. Here, we infer the mixture of ways polygenic effects on physiological traits covary between males and females. We find that GxSex is pervasive but acts primarily through systematic sex differences in the magnitude of many genetic effects (″amplification″), rather than in the identity of causal variants. Amplification patterns account for sex differences in trait variance. In some cases, testosterone may mediate amplification. Finally, we develop a population-genetic test linking GxSex to contemporary natural selection and find evidence for sexually antagonistic selection on variants affecting testosterone levels. Taken together, our results suggest that the amplification of polygenic effects is a common mode of GxSex that may contribute to sex differences and fuel their evolution.