Molecular dynamics simulations are employed to investigate the radial compression behavior of multi-walled carbon nanotubes (MWCNTs), with a particular focus on the coupled effects of tube diameter and wall number. By analyzing the average radial and hoop forces on each wall together with the evolution of atomic potential energy, the inter-wall mechanical interactions during radial expansion are clearly elucidated. The results indicate that the radial stiffness of MWCNTs exhibits a pronounced size dependence on tube diameter: smaller-diameter nanotubes display significantly higher radial stiffness due to enhanced atomic curvature, while increasing the wall number markedly improves the overall load-bearing capacity. This study further reveals that an obvious wall-by-wall load-transfer lag phenomenon occurs during the radial compression of MWCNTs. This effect becomes more pronounced with increasing wall number, resulting in the inner walls maintaining relatively low force levels throughout the compression process. In addition, potential energy analysis shows that energy accumulation is highly concentrated in the outer walls, whereas the inner walls remain at relatively low energy levels even under large deformations. These findings offer new insights into regulating the radial mechanical response of multi-walled carbon nanotubes through curvature and interlayer van der Waals interactions. They provide theoretical guidance for the design of high-performance nanodevices and pressure-resistant nanostructures, while opening new avenues for the theoretical modeling and experimental validation of pressure sensors and interface-enhanced composites.