Graphene on transition-metal dichalcogenides exhibits proximity spin-orbit effects opening new venues for optospintronics, and provides route for exploring robust helical edge states. Some of the transition-metal dichalcogenides showing metal-insulator transition and the sequence of different charge density wave transformations. In such a case a fascinating finding is observed as the induced proximity effects in graphene are significantly influenced by the presence of the commensurate charge density wave. We present our first-principles results for the electronic band structures and suggest relevant orbital and spin-orbital proximity effects by means of phenomenological symmetry-based Hamiltonians.