Weighted-cscK metrics provide a universal framework for the study of canonical metrics, e.g., extremal metrics, Kahler-Ricci soliton metrics, \mu-cscK metrics. In joint works with Yaxiong Liu, we prove that on a Kahler manifold X, the G-coercivity of weighted Mabuchi functional implies the existence of weighted-cscK metrics.  In particular, there exists a weighted-cscK metric if X is a projective manifold that is weighted K-stable for models.  We will also discuss some progress on singular varieties.