The demand for low contact resistance in two-dimensional (2D) nanoelectronics has positioned semimetals as ideal contact materials, owing to their ability to minimize the formation of metal-induced gap states (MIGS). While the contact physics of Dirac semimetals is well understood, type-II Weyl (i.e., Weyl-II) semimetals remain largely unexplored, despite their unique potential for achieving defect-free nanoscale devices. Here, using density functional theory (DFT), we elucidate the interfacial physics of MoS2-Weyl-II semimetal junctions and conduct a comparative analysis with Dirac semimetals. Crucially, we identify a downward extension of the conduction band minimum (CBM) in MoS2, originating from contact-induced interfacial states. This phenomenon is closely tied to the rectangular Brillouin zone of Weyl-II semimetals, which-unlike the 3-fold symmetry of MoS2 and Dirac semimetals-renders orbital hybridization in MoS2-Weyl-II systems highly sensitive to contact angles. By introducing a modified Schottky-Mott rule that accounts for vacuum level shifts, CBM extensions, and orbital interactions, we significantly improve conventional Schottky barrier height predictions. This approach effectively resolves longstanding theoretical-experimental discrepancies, providing a robust framework to properly design and optimize 2D contacts in next-generation logic devices.