Body size is a key physiological, ecological, and evolutionary characteristic of species. Within most major clades, body size distributions follow a right-skewed pattern where most species are relatively small while a few are orders of magnitude larger than the median size. Using a novel database of 742 extant and extinct primate species' sizes over the past 66 million years, we find that primates exhibit the opposite pattern: a left-skewed distribution. We investigate the long-term evolution of this distribution, first showing that the initial size radiation is consistent with plesiadapiformes (an extinct group with an uncertain ancestral relationship to primates) being ancestral to modern primates. We calculate the strength of Cope's Rule, showing an initial tendency for descendants to increase in size relative to ancestors until the trend reverses 40 million years ago. We explore when the primate size distribution becomes left-skewed and study correlations between body size patterns and climactic trends, showing that across Old and New World radiations the body size distribution initially exhibits a right-skewed pattern. Left-skewness emerged early in Old World primates in a manner consistent with a previously unidentified possible maximum body size, which may be mechanistically related to primates' encephalization and complex social groups.