  We investigate the distribution of eigenvalues of the weighted Laplacian on
closed weighted Riemannian manifolds of nonnegative Bakry-\'Emery Ricci
curvature. We derive some universal inequalities among eigenvalues of the
weighted Laplacian on such manifolds. These inequalities are quantitative
versions of the previous theorem by the author with Shioya. We also study some
geometric quantity, called multi-way isoperimetric constants, on such manifolds
and obtain similar universal inequalities among them. Multi-way isoperimetric
constants are generalizations of the Cheeger constant. Extending and following
the heat semigroup argument by Ledoux and E. Milman, we extend the Buser-Ledoux
result to the $k$-th eigenvalue and the $k$-way isoperimetric constant. As a
consequence the $k$-th eigenvalue of the weighted Laplacian and the $k$-way
isoperimetric constant are equivalent up to polynomials of $k$ on closed
weighted manifolds of nonnegative Bakry-\'Emery Ricci curvature.
