Lead halide perovskite nanocrystals (NCs) have attracted much attention as light-source materials for light-emitting diodes, lasers, and quantum light emitters. The luminescence properties of perovskite NCs and the performance of NC-based light-source devices depend on trion and biexciton dynamics. Here, we examined the size dependence of trion and biexciton binding energies by conducting low-temperature single-dot spectroscopy on three different perovskite NCs: CsPbBr3, CsPbI3, and FAPbBr3. While the photoluminescence spectral widths of the all-inorganic CsPbBr3 and CsPbI3 NCs were narrow, compared with those of the organic-inorganic hybrid FAPbBr3 NCs, the binding energies of trions and biexcitons of all three samples showed similar size dependences, independent of the A-site cation and halogen. The effective-mass approximation calculations implied the importance of dynamical dielectric screening on the formation of trions and biexcitons.