This paper addresses a weighted localized scheme and its application to the hierarchical clustering architecture, which results in reduced overlapping areas of clusters. Our previous proposed scheme, Low-Energy Localized Clustering (LLC), dynamically regulates the radius of each cluster for minimizing energy consumption of cluster heads (CHs) while the entire network field is still being covered by each cluster in sensor networks. We present weighted Low-Energy Localized Clustering(w-LLC), which has better efficiency than LLC by assigning weight functions to each CH. Drew on the w-LLC scheme, weighted Localized Clustering for RFID networks(w-LCR) addresses a coverage-aware reader collision arbitration protocol as an application. w-LCR is a protocol that minimizes collisions by minimizing overlapping areas of clusters.