Baryon stopping and particle production in Pb+Pb collisions at 158 GeV/nucleon are studied as a function of the collision centrality using new proton, antiproton, charged kaon and charged pion production data measured with the NA49 experiment at the CERN Super Proton Synchrotron (SPS). Stopping, which is measured by the shift in rapidity of net protons or baryons from the initial beam rapidity, increases in more central collisions. This is expected from a geometrical picture of the collisions. The stopping data are quantitatively compared to models incorporating various mechanisms for stopping. In general, microscopic transport calculations which incorporate current theoretical models of baryon stopping or use phenomenological extrapolations from simpler systems overestimate the dependence of stopping on centrality. Approximately, the yield of produced pions scales with the number of nucleons participating in the collision. A small increase in yield beyond this scaling, accompanied by a small suppression in the yield of the fastest pions, reflects the variation in stopping with centrality. Consistent with the observations from central collisions of light and heavy nuclei at the SPS, the transverse momentum distributions of all particles are observed to become harder with increasing centrality. This effect is most pronounced for the heaviest particles. This hardening is discussed in terms of multiple scattering of the incident nucleons of one colliding nucleus as they traverse the other nucleus and in terms of rescattering within the system of produced particles.