We present the results from a spectroscopic survey for intervening MgII absorption in the spectra of 381 background QSOs conducted at the Multiple Mirror Telescope. This survey complements our earlier SDSS EDR MgII survey, extending our results to lower redshift ($z simeq 0.15$) and weaker MgII $lambda2796$ rest equivalent width ($W_0^{lambda2796} simeq 0.1$AA). We confirm two major results from that survey: the transition in the $W_0^{lambda2796}$ distribution at $W_0^{lambda2796} approx 0.3$AA, and the $W_0^{lambda2796}$-dependent evolution of the incidence of systems. The nature of $partial^2N/partial z partial W_0^{lambda2796}$ is consistent with the idea that multiple physically-distinct components/processes contribute to the incidence of MgII absorption systems in a $W_0$-dependent manner and evolve at different rates. A significant decrease in the total proper absorption cross section is detected in our MMT data for systems as weak as 1.0 AA $le W_0^{lambda2796} < 1.5$AA at $zlesssim 0.4$. We discuss this $W_0$-dependent evolution in the context of the evolution of galaxy structures, processes including superwinds and interactions, and damped-Ly$alpha$ absorbers. We also consider the possibility that the observed redshift and $W_0^{lambda2796}$ dependence of the incidence of absorption in spectroscopic surveys for low-ion/neutral gas results from the effects of dust-induced extinction.
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