The sensitivity of petrophysical parameters such as porosity and permeability to stress conditions is critical in unconventional reservoir management. Calculation of these dependencies on stress conditions that arise during oil and gas production operations remains a challenge, and despite its importance, is still poorly understood. This study focuses on the quantification of stress-dependent porosity and permeability evolution based on pore size distributions, and validation of the proposed model. To better understand the pore structure dynamic evolution and link it to rock properties, i.e. pore type, shape, and mineral composition, two tight sandstone and two shale rock samples were characterized. First, samples were assessed via Field Emission-Scanning Electron Microscopy (FE-SEM). Then, porosity and permeability were measured at different confining pressures. As proxy for the pore structure, the pore-size distribution (PSD) was determined via interpretation of the nuclear magnetic resonance (NMR) T2 distribution. Results show that porosity and permeability decrease as the effective stress is increased, as anticipated. The detailed analysis shows that this dependence is dominated by the percentage of clay and organic matter, and the initial microstructure. Here, we proposed a connection between rock microstructure and petrophysical properties that relies on PSD, which in turn connects the T2 distributions to stress-dependent porosity and permeability. The proposed stress sensitivity model that accounts for changes in PSD agrees well with the experimental data, better than predictions using other models. Our findings contribute to the understanding of dynamic rock petrophysical evolution and the response to the pore/fracture deformation with the adjustment of stress in subsurface activities.