Karamanis (2001), Kibble (2001), and Beaver (2004), have argued for a ranking of the centering principles as opposed to weighting, and indeed Beaver provides a unified formulation of the centering rules and constraints as a ranked set of OT constraints.
we believe that such a ranking stands in need of empirical justification, and Beaver's data actually provide little evidence for strict ranking as opposed to weighting of constraints (see Kibble 2003).