Colonizing weed populations face novel selective environments, which may drive rapid shifts in life history. These shifts may be amplified when colonists are hybrids of species with divergent life histories. Selection on such phenotypically diverse hybrids may create highly fecund weeds. We measured the phenotypic variation, strength of natural selection and evolutionary response of hybrid and nonhybrid weeds. We created F1 hybrids of wild radish, an early flowering, small-stemmed weed, and its late-flowering, large-stemmed, crop relative (Raphanus spp.). Replicate wild and hybrid populations were established in an agricultural landscape in Michigan, USA. The consequences of three generations of natural selection were measured in a common garden experiment. Hybrid populations experienced strong selection for larger, earlier flowering plants whereas selection was relatively weak on wild populations. Large plant size evolved two to three times faster in the hybrid populations than in wild populations, yet hybrid populations did not evolve earlier flowering. Strong selection on size and phenotypic correlations between age at reproduction and size may have limited the response of flowering phenology. Our findings demonstrate hybridization between species with divergent life histories may catalyse the rapid evolution of certain adaptive, weedy traits while tradeoffs limit the evolution of others.