  Let $(M,g)$ be a complete non-compact Riemannian manifold together with a
function $e^h$, which weights the Hausdorff measures associated to the
Riemannian metric. In this work we assume lower or upper radial bounds on some
weighted or unweighted curvatures of $M$ to deduce comparisons for the weighted
isoperimetric quotient and the weighted capacity of metric balls in $M$
centered at a point $o\in M$. As a consequence, we obtain parabolicity and
hyperbolicity criteria for weighted manifolds generalizing previous ones. A
basic tool in our study is the analysis of the weighted Laplacian of the
distance function from $o$. The technique extends to non-compact submanifolds
properly immersed in $M$ under certain control on their weighted mean
curvature.
