Intrasexual selection through male competition favoring larger male body size is the preferred explanation for the evolution and maintenance of male-biased sexual size dimorphism among polygynous species. Although sexual selection has been well studied in some groups of lizards, sexual selection in the nine species of lava lizards (Microlophus spp.) of the Galápagos has received little attention. The purpose of this research was to test the importance of male body size in the context of sexual selection by both sexes. Using three different sizes of robotic models capable of emulating the appearance and display patterns of male San Cristóbal Lava Lizards (M. bivittatus), we analyzed the responses that the models elicited among free-ranging lizards of the same sex (confrontation) and opposite sex (courtship). Results showed that body size of both male lizards and robotic antagonists influenced the number of displays performed by males. Male body size positively influenced the number of aggressive responses, scaling with the size of the opponent. The model representing larger lizards received higher display counts from males. Body size of robotic models, but not female lizards, influenced the number of displays performed by females. Females responded the most to the small and large models. Display intensity was not affected by any of the variables considered for either sex. Results from this study support the hypothesis that male-biased sexual size dimorphism in M. bivittatus is driven at least in part by both intrasexual and intersexual selection favoring larger male body size.