The alkali fullerides, A(3)C(60) (A = alkali metal) are molecular superconductors that undergo a transition to a magnetic Mott-insulating state at large lattice parameters. However, although the size and the symmetry of the superconducting gap, Δ, are both crucial for the understanding of the pairing mechanism, they are currently unknown for superconducting fullerides close to the correlation-driven magnetic insulator. Here we report a comprehensive nuclear magnetic resonance (NMR) study of face-centred-cubic (f.c.c.) Cs(3)C(60) polymorph, which can be tuned continuously through the bandwidth-controlled Mott insulator-metal/superconductor transition by pressure. When superconductivity emerges from the insulating state at large interfullerene separations upon compression, we observe an isotropic (s-wave) Δ with a large gap-to-superconducting transition temperature ratio, 2Δ0/k(B)T(c) = 5.3(2) [Δ0 = Δ(0 K)]. 2Δ0/k(B)T(c) decreases continuously upon pressurization until it approaches a value of ~3.5, characteristic of weak-coupling BCS theory of superconductivity despite the dome-shaped dependence of Tc on interfullerene separation. The results indicate the importance of the electronic correlations for the pairing interaction as the metal/superconductor-insulator boundary is approached.