Experiments comparing conventional and organic systems often report similar yields despite substantially higher weed abundance in the organic systems. A potential explanation for this observation is that weed-crop competition relationships differ between the two types of systems. We analysed weed and crop yield data from the Rodale Institute Farming Systems Trial (FST), which provides a unique 27-year dataset of a conventional (CNV) and two organic [manure (MNR) and legume (LEG)] soyabean (Glycine max (L.) Merr.) and maize (Zea mays L.) cropping systems. Average soyabean yields were similar between the MNR and CNV systems and only slightly reduced in the LEG system, whereas average maize yields did not differ among systems despite the two organic systems having more than four and six times greater weed biomass in soyabean and maize respectively. Plot-level weed biomass-crop yield relationships indicated that weed-crop competition differed between the two organic and CNV systems in maize, and was strongest in the CNV system, intermediate in the LEG system and weakest in the MNR system. These results suggest that organic cropping systems may be able to tolerate a greater abundance of weeds compared to conventional systems and that fertility management within organic systems may influence weed-crop competition.