In this work, we demonstrate for the first time the importance of weak pi-stacking interactions in modulating cl the two-photon absorption (TPA) process of a fullerene-buckycatcher inclusion complex. To unfold the role of weak interactions on the TPA cross-section, we have used the range-separated Coulomb-attenuating method B3LYP functional (CAMB3LYP) for all time-dependent density functional theory Calculations. Our calculations suggest that whereas the buckycatcher has very strong TPA active modes at shorter wavelengths, the TPA modes in the fullerene are very weak but have absorption wavelengths that are in the infrared (IR) or near-IR region of the spectrum. Remarkably, the TPA cross-section of the fullerene-buckycatcher (F-C) supramolecule is quite large at desirable near-IR wavelengths. The overall investigation emphasizes the fact that the limitations of buckycatcher and fullerene as promising TPA active materials can be resolved if one uses the weakly coupled F-C supramolecule instead of considering them individually.