Weed management is a major challenge in organic crop production, and organic farms generally harbor larger weed populations and more diverse communities compared with conventional farms. However, little research has been conducted on the effects of different organic management practices on weed communities and crop yields. In 2014 and 2015, we measured weed community structure and soybean [Glycine max (L.) Merr.] yield in a long-term experiment that compared four organic cropping systems that differed in nutrient inputs, tillage, and weed management intensity: (1) high fertility (HF), (2) low fertility (LF), (3) enhanced weed management (EWM), and (4) reduced tillage (RT). In addition, we created weed-free subplots within each system to assess the impact of weeds on soybean yield. Weed density was greater in the LF and RT systems compared with the EWM system, but weed biomass did not differ among systems. Weed species richness was greater in the RT system compared with the EWM system, and weed community composition differed between RT and other systems. Our results show that differences in weed community structure were primarily related to differences in tillage intensity, rather than nutrient inputs. Soybean yield was lower in the EWM system compared with the HF and RT systems. When averaged across all four cropping systems and both years, soybean yield in weed-free subplots was 10% greater than soybean yield in the ambient weed subplots that received standard management practices for the systems in which they were located. Although weed competition limited soybean yield across all systems, the EWM system, which had the lowest weed density, also had the lowest soybean yield. Future research should aim to overcome such trade-offs between weed control and yield potential, while conserving weed species richness and the ecosystem services associated with increased weed diversity.