The development of power-efficient spintronic devices has been a compelling need in the post-CMOS technology era. The effective tuneability of spin-orbit coupling (SOC) in the bulk and at the interfaces of hybrid material stacks is a prerequisite for scaling down the dimensions and power consumption of these devices. In this work, we demonstrate the strong chemisorption of C60 (fullerene) molecules when grown on the high-SOC 𝛽-W layer. The parent Co20⁢Fe60⁢B20/𝛽-W (CFB/⁢𝛽-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 𝛽-W reduces the effective Gilbert damping by  ∼15% in CFB/⁢𝛽-W/C60 heterostructures. The antidamping is accompanied by a gigantic  ∼115% enhancement in the spin-pumping-induced output voltage owing to molecular hybridization. The noncollinear density-functional-theory calculations confirm the long-range enhancement of the SOC of 𝛽-W upon the chemisorption of C60 molecules, which in turn can also enhance the SOC at the CFB/⁢𝛽-W interface in CFB/⁢𝛽-W/C60 heterostructures. The combined amplification of the bulk as well as the interfacial SOC upon molecular hybridization stabilizes the antidamping and enhanced spin-to-charge conversion, which can pave the way for the fabrication of power-efficient spintronic devices.