We present results of atomic-force-microscopy-based friction measurements on Re-doped molybdenum disulfide (MoS2). In stark contrast to the widespread observation of decreasing friction with increasing number of layers on two-dimensional (2D) materials, friction on Re-doped MoS2 exhibits an anomalous, i.e., inverse dependence on the number of layers. Raman spectroscopy measurements combined with ab initio calculations reveal signatures of Re intercalation. Calculations suggest an increase in out-of-plane stiffness that inversely correlates with the number of layers as the physical mechanism behind this remarkable observation, revealing a distinctive regime of puckering for 2D materials.