Cope's rule proposes that animal lineages evolve toward larger body size over time. To test this hypothesis across all marine animals, we compiled a data set of body sizes for 17,208 genera of marine animals spanning the past 542 million years. Mean biovolume across genera has increased by a factor of 150 since the Cambrian, whereas minimum biovolume has decreased by less than a factor of 10, and maximum biovolume has increased by more than a factor of 100,000. Neutral drift from a small initial value cannot explain this pattern. Instead, most of the size increase reflects differential diversification across classes, indicating that the pattern does not reflect a simple scaling-up of widespread and persistent selection for larger size within populations.