Bulk molybdenum disulfide is known to be a nonmagnetic material. We have synthesized edge-oriented MoS2 nanosheet-like films that exhibit weak magnetism ( approximately 1-2 emu/g) and 2.5% magnetoresistance effects with a Curie temperature of 685 K. The magnetization is related to the presence of edge spins on the prismatic edges of the nanosheets. Spin-polarized calculations were performed on triangular-shaped cluster models in order to provide insight into the origin of magnetism on the edges as well as the size-property correlation in these MoS2 nanosheets. Our results imply that nanostructured films with a high density of edge spins can give rise to magnetism even though the bulk material is nonmagnetic.