Many spectacular cases of biological diversity are associated with sexual selection, and structures under sexual selection often show positive static allometry: they are disproportionately large for the size of the animal’s body in larger individuals. Other sexually selected structures, however, show negative allometry or isometry. Theory fails to account for this variation and recent summaries do not agree regarding the frequency of positive allometry in sexually selected structures. We propose explanations for why sexually selected structures with different functions (courtship, threat signals, and weapons) should differ in allometry. Positive allometry is predicted for threat structures (including most weapons) because larger individuals tend to win fights and threat signals are used to avoid unwinnable fights with larger opponents, the reproductive payoffs for contests tend to be higher for larger males, and discriminating the sizes of relatively larger traits requires greater absolute differences due to Weber’s Law of sensory physiology. Male courtship signals, in contrast, convey many types of information, much of which is not consistently related to male size, so positive allometry is expected less often. We tested these predictions empirically by comparing the allometries of male structures with relatively “pure” functions. Our predictions were confirmed, thus helping to explain differences in previous empirical surveys.