Concentration is one of the key dark matter halo properties that could drive the scatter in the stellar-to-halo mass relation of massive clusters. We derive robust photometric stellar masses for a sample of brightest central galaxies (BCGs) in SDSS redMaPPer clusters at $0.17<z<0.3$, and split the clusters into two equal-halo mass subsamples by their BCG stellar mass $M_*$. The weak lensing profiles $DeltaSigma$ of the two cluster subsamples exhibit different slopes on scales below 1 M$pc/h$. To interpret such discrepancy, we perform a comprehensive Bayesian modelling of the two $DeltaSigma$ profiles by including different levels of miscentring effects between the two subsamples as informed by X-ray observations. We find that the two subsamples have the same average halo mass of $1.74 times 10^{14} M_{odot}/h$, but the concentration of the low-$M_*$ clusters is $5.87_{-0.60}^{+0.77}$, ${sim}1.5sigma$ smaller than that of their high-$M_*$ counterparts~($6.95_{-0.66}^{+0.78}$). Furthermore, both cluster weak lensing and cluster-galaxy cross-correlations indicate that the large-scale bias of the low-$M_*$, low-concentration clusters are ${sim}10%$ higher than that of the high-$M_*$, high-concentration systems, hence possible evidence of the cluster assembly bias effect. Our results reveal a remarkable physical connection between the stellar mass within 20{-}30 k$pc/h$, the dark matter mass within ${sim}$ 200 k$pc/h$, and the cosmic overdensity on scales above 10 M$pc/h$, enabling a key observational test of theories of co-evolution between massive clusters and their central galaxies.
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