  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 $\Delta\Sigma$ 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 $\Delta\Sigma$ 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 $5.87_{-0.60}^{+0.77}$, ${\sim}1.5\sigma$ 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.
