  In a previous paper, we showed that the blowup of a weighted extremal
K\"ahler manifold at a relatively stable fixed point admits a weighted extremal
metric. Using this result, we prove that a weighted extremal manifold is
relatively weighted K-polystable. In particular, a weighted cscK manifold is
weighted K-polystable. This strengthens both the weighted K-semistability
proved by Lahdili and Inoue, and the weighted K-polystability with respect to
smooth degenerations by Apostolov--Jubert--Lahdili, allowing for possibly
singular degenerations.
