Comparison Theorems on Weighted Finsler Manifolds and Spacetimes with <i>?</i>-Range

We establish the Bonnet-Myers theorem, Laplacian comparison and Bishop-Gromov volume theorem for weighted Finsler manifolds as well spacetimes, of Ricci curvature bounded below by using weight function. These theorems are formulated with $\epsilon$-range introduced in our previous paper, that provides a natural viewpoint interpolating conditions different effective dimensions. Some results new even Riemannian generalize Wylie-Yeroshkin Kuwae-Li.