Understanding the rates of weathering, and more generally dissolution and precipitation in porous materials, is important for many applications including modeling the global carbon cycle and predicting short-term and long-term behavior in subsurface carbon sequestration sites. However, interpretation of the rates remains elusive as they have been observed to vary with location, measurement procedure, and time. We argue that the mechanisms responsible for the apparent aging in the rates, or gradual decrease over time, can be partially determined by noting which measure of time best characterizes the dependence. If the rate is best described as a function of residence time, then hydraulic and transport limitations are responsible for the variations. If reaction age is a better independent variable, then limitations in the chemical reaction at the fluid-mineral interface are responsible. We discuss several mechanisms in each category and construct mathematical models that demonstrate quantitatively how they affect time variation in reaction rates. These include nonlinear kinetics, disordered kinetics, and a reprecipitation model that accounts for the limited access to the bulk of a dissolving solid. We apply the reprecipitation model to the development of the isotopic composition of porous solids to derive an apparent rate constant that decays with inverse time, similar to that calculated for diagenesis in deep-sea sediments. This paper provides a theoretical framework for understanding the changing and varied dissolution and precipitation rates measured in the laboratory and in nature, and provides testable quantitative models that capture the aging effect.