Cover crops included in a crop rotation can help increase nitrogen (N) availability to subsequent crops, raise soil organic matter, and suppress emergence and growth of various weed species. However, weed suppression by cover crops has mostly been investigated shortly after cover crop termination and not over a longer period spanning into the next cropping season. The effects of sunn hemp (Crotalaria juncea) and sorghum-sudangrass (Sorghum ×drummondi) planted the previous year on N availability before transplanting of late summer cabbage (Brassica oleracea), weed germination and growth, and cabbage yield was examined in field studies conducted in 2018 and 2019 at Pittstown, NJ. Results established that there was little evidence for a functional difference in soil N availability for fall cabbage production because of previous cover crop type. Heavy rainfall events both years may have caused major losses of available N that might otherwise be expected to come from N mineralization of residues of legume cover crop like sunn hemp. During the cover crop season, smooth pigweed (Amaranthus hybridus) and common lambsquarters (Chenopodium album) dry biomass was 77% and 82% lower, respectively, in sorghum-sudangrass compared with sunn hemp plots. The subsequent season following sorghum-sudangrass cover crop, dry biomass of broadleaf weeds was lower by 74% and 56% in June and July, respectively, compared with preceding sunn hemp. Smooth pigweed, common lambsquarters, and hairy galinsoga (Galinsoga quadriradiata) were the weed species most consistently affected by preceding sorghum-sudangrass cover crop with biomass decreased by up to 80%, 78%, and 64%, respectively. Thus, it appears that sorghum-sudangrass can provide suppression of some broadleaf species over a relatively long period and is indicative of sorghum-sudangrass allelopathic activity. On the contrary, density and biomass of grassy weeds as well as commercial yield of transplanted cabbage were unaffected by the preceding cover crop. These results suggest that sorghum-sudangrass cover crop could be integrated to transplanted cole crop rotation for providing weed suppression benefits without altering crop yield in New Jersey organic vegetable cropping systems.