  In this paper, we prove some Willmore-type inequalities for closed
hypersurfaces in weighted manifolds with nonnegative Bakry-\'Emery Ricci
curvature. In particular, we give a sharp Willmore-like inequality in shrinking
gradient Ricci solitons. We also characterize the equality cases of our
Willmore-type inequalities. These results can be regarded as generalizations of
Agostiniani-Fogagnolo-Mazzieri's Willmore-type inequality to weighted
manifolds. As applications, we derive some isoperimetric type inequalities
under certain existence assumptions of isoperimetric regions in weighted
manifolds.
