We investigate how variations in a planet’s size and the chemical (mineral) composition of its upper mantle and surface affect processes involved in the carbonate-silicate cycle, which is thought to have regulated the composition of Earth’s atmosphere and its surface temperature over geologic time. We present models of geophysical and geochemical controls on these processes: outgassing, continental weathering, and seafloor weathering, and analyze sensitivities to planet size and composition. For Earth-like compositions, outgassing is maximized for planets of Earth’s size. Smaller planets convect less vigorously; higher pressures inside larger planets hinder melting. For more felsic mantles, smaller planets (0.5-0.75 Earth mass) outgas more, whereas more mafic planets follow the size trend of Earth’s composition. Planet size and composition can affect outgassing by two orders of magnitude, with variability driven by mass in the first 2.5 Gyr after formation and by composition past that time. In contrast, simulations spanning the diversity of surface compositions encountered in the inner solar system indicate that continental weathering fluxes are about as sensitive to surface composition or the patchiness of land as they are to surface temperature, with fluxes within a factor of five of Earth’s. Seafloor weathering appears more sensitive to uncertainties in tectonic regime (occurrence, speed, and size of plates) than to seafloor composition. These results form a basis to interpret calculations of geological surface carbon fluxes to track atmospheric compositions, through time, of lifeless exo-Earths, providing a baseline against which the effect of biological activity may be distinguished with telescopic observations.