Development of power efficient spintronics devices has been the compelling need in the post-CMOS technology era. The effective tunability of spin-orbit-coupling (SOC) in bulk and at the interfaces of hybrid materials stacking is a prerequisite for scaling down the dimension and power consumption of these devices. In this work, we demonstrate the strong chemisorption of C60 molecules when grown on the high SOC $\beta$-W layer. The parent CFB/$\beta$-W bilayer exhibits large spin-to-charge interconversion efficiency, which can be ascribed to the interfacial SOC observed at the Ferromagnet/Heavy metal interface. Further, the adsorption of C60 molecules on $\beta$-W reduces the effective Gilbert damping by $\sim$15% in the CFB/$\beta$-W/C60 heterostructures. The anti-damping is accompanied by a gigantic $\sim$115% enhancement in the spin-pumping induced output voltage owing to the molecular hybridization. The non-collinear Density Functional Theory calculations confirm the long-range enhancement of SOC of $\beta$-W upon the chemisorption of C60 molecules, which in turn can also enhance the SOC at the CFB/$\beta$-W interface in CFB/$\beta$-W/C60 heterostructures. The combined amplification of bulk as well interfacial SOC upon molecular hybridization stabilizes the anti-damping and enhanced spin-to-charge conversion, which can pave the way for the fabrication of power efficient spintronics devices.