Two-dimensional (2D) layered materials have shown layer-dependent optical properties in both linear optical and nonlinear optical (NLO) regimes due to prominent interlayer coupling and quantum confinement in an atomic scale. However, the NLO properties become more complicated as both saturable absorption (SA) and reverse saturable absorption (RSA) easily happen in 2D materials, which results in a significant challenge to understand the evolution of nonlinear absorption with layers. Motivated by this, chemical vapor-deposited chalcogenide compounds (WS2, MoS2, and Bi2S3) are used to investigate the pump intensity and layer number-dependent NLO properties. The values of nonlinear absorption coefficients of these chalcogenide compounds increase with the pump intensity by an 800 nm femtosecond laser, which can be described by an empirical power law function. The SA process due to the large transition probability of the ground state readily takes place in thick samples, while RSA occurs easily in thin samples due to the two-photon absorption (TPA). The transition from TPA to SA is deduced to occur at 13L-WS2, 15L-MoS2, and 5L-Bi2S3, which is related to the layer-dependent band gaps. Our results provide an efficient way to tune optical nonlinearities with a controlled layer number and to design corresponding NLO devices such as optical switches and saturable absorbers.