Sweet potato (Ipomoea batatas L.) is one of the most important global food crops. This crop exhibits excellent allelopathic potential against various weeds, but its allelopathic mechanism at the molecular level is unclear. Therefore, metabolomic and transcriptomic analyses were performed to explore the allelopathic effects, metabolic pathway, and associated genes for two major compounds with allelopathic activity, palmitic acid and linoleic acid. The sweet potato variety Ningshu 25 was employed in the current study. The results showed that palmitic acid and linoleic acid had strong allelopathic effects on seed germination, plant growth, antioxidant enzyme activity, and chlorophyll content of two weeds Digitaria sanguinalis and Bidens pilosa. The content of the two targeted metabolites was affected by different environmental conditions and was significantly increased under low temperature (15 °C). Five metabolic pathways involved in the two targeted metabolites of fatty acids were found: fatty acid biosynthesis, fatty acid elongation, fatty acid degradation, biosynthesis of cutin, suberine, and wax, and the linoleic acid metabolism pathway. The synthesis of palmitic acid is significantly enriched in the biosynthesis pathways of fatty acids, cutin, suberine, and wax, and the synthesis of linoleic acid is significantly enriched in the linoleic acid metabolism pathway. Under different environmental conditions, there were three key genes expressed—g4988, g11881, and g19673—located in the biosynthesis pathways of cutin, suberine, and wax; four key genes expressed—g31191, g60956, g49811, and g59542—located in the biosynthesis pathway of fatty acids; and six key expressed genes—g26575, g24787, g23517, g57649, g58562, and g4314—located in biosynthesis pathway of linoleic acid, respectively. Our study advances understanding of the molecular mechanisms behind allelopathic traits in sweet potato and provides a set of candidate genes for use in improving allelopathic potential in sweet potato germplasm resources.