Body size is often assumed to represent the outcome of conflicting selection pressures of natural and sexual selection. Marine iguana (Amblyrhynchus cristatus) populations in the Galápagos exhibit 10-fold differences in body mass between island populations. There is also strong sexual size dimorphism, with males being about twice as heavy as females. To understand the evolutionary processes shaping body size in marine iguanas, we analyzed the selection differentials on body size in two island populations (max. male mass 900 g in Genovesa, 3500 g in Santa Fé). Factors that usually confound any evolutionary analysis of body sizes-predation, interspecific food competition, reproductive role division-are ruled out for marine iguanas. We show that, above hatchlings, mortality rates increased with body size in both sexes to the same extent. This effect was independent of individual age. The largest animals (males) of each island were the first to die once environmental conditions deteriorated (e.g., during El Niños). This sex-biased mortality was the result of sexual size dimorphism, but at the same time caused sexual size dimorphism to fluctuate. Mortality differed between seasons (selection differentials as low as -1.4) and acted on different absolute body sizes between islands. Both males and females did not cease growth when an optimal body size for survival was reached, as demonstrated by the fact that individual adult body size phenotypically increased in each population under favorable environmental conditions beyond naturally selected limits. But why did marine iguanas grow 'too large' for survival? Due to lek mating, sexual selection constantly favored large body size in males (selection differentials up to +0.77). Females only need to reach a body size sufficient to produce surviving offspring. Thereafter, large body size of females was less favored by fertility selection than large size in males. Resulting from these different selection pressures on male and female size, sexual size dimorphism was mechanistically caused by the fact that females matured at an earlier age and size than males, whereafter they constantly allocated resources into eggs, which slowed growth. The observed allometric increase in sexual size dimorphism is explained by the fact that the difference between these selective processes becomes larger as energy abundance in the environment increases. Because body size is generally highly heritable, these selective processes are expected to lead to genetic differences in body size between islands. We propose a common-garden experiment to determine the influence of genetic factors and phenotypic reaction norms of final body size.