Larger body size has long been assumed to correlate with greater risk of extinction, helping to shape body size distributions across the tree of life, but lack of comprehensive size data for fossil taxa have left this hypothesis untested for most higher taxa across the vast majority of evolutionary time. Here we assess the relationship between body size and extinction using a dataset comprising the body sizes, stratigraphic ranges, and occurrence patterns of 9,408 genera of fossil marine animals spanning eight Linnaean classes across the past 485 million years. We find that preferential extinction of smaller-bodied genera within classes is substantially more common than expected due to chance and that there is little evidence for preferential extinction of larger-bodied genera. Using a capture-mark-recapture analysis, we find that this size bias of extinction persists even after accounting for a pervasive bias against the sampling of smaller-bodied genera within classes. The size bias in extinction also persists after including geographic range as an additional predictor of extinction, indicating that correlation between body size and geographic range does not provide a simple explanation for the association between size and extinction. Regardless of the underlying causes, the preferential extinction of smaller-bodied genera across many higher taxa and most of geological time indicates that the selective loss of large-bodied animals is the exception, rather than the rule, in the evolution of marine animals.