The basis set limit electronic binding energies of He-2, (HF)(2), and (H2O)(2) at the MP2 and CCSD(T) level (coupled cluster single and double excitations with perturbative triples correction) were estimated through the extrapolation of two successive energies of the dimer with correlation-consistent aug-cc-pVXZ (X=D(2),T(3),Q(4),5,6) basis sets by 1/X-p, where the convergence power p was derived from the basis set convergence behavior of the monomer (He, HF, and H2O) energies toward the known corresponding basis set limits. It is shown that the convergence behaviors of the correlation energy of the monomer and dimer with correlation-consistent basis sets closely resemble each other in these weakly bound systems, which is well demonstrated by the excellent agreement of the estimated basis set limit binding energies on this premise with the reference values in all cases. By contrast, the accuracy of a simple two-point 1/X-3 extrapolation scheme in estimating the binding energies of these complexes is shown to depend on the correlation level, basis set quality, and kind of interatomic or molecular interactions present in the system. For the extrapolation of correlation energies of the dimer with aug-cc-pVDZ and aug-cc-pVTZ basis set by 1/X-p with the convergence power p determined from the basis set convergence behavior of the monomer correlation energies, the estimated MP2 binding energies for He-2, (HF)(2), and (H2O)(2) are 19.5 muE(h)(21.4), 7.00 mE(h)(7.04), and 7.79 mE(h)(7.82), with the values in parentheses representing the exact basis set limit binding energies. The corresponding CCSD(T) binding energies for He-2, (HF)(2), and (H2O)(2) are 30.8 muE(h)(33.8), 7.19 mE(h)(7.21), and 7.86 mE(h)(7.88), respectively.