The evolution of anvil clouds detrained from deep convective systems has important implications for the tropical energy balance and is thought to be shaped by radiative heating. We use combined radar-lidar observations and a radiative transfer model to investigate the influence of radiative heating on anvil cloud altitude, thickness, and microphysical structure. We find that high clouds with an optical depth between 1 and 2 are prevalent in tropical convective regions and can persist far from any convective source. These clouds are generally located at higher altitudes than optically thicker clouds, experience strong radiative heating, and contain high concentrations of ice crystals indicative of turbulence. These findings support the hypothesis that anvil clouds are driven towards and maintained at a preferred optical thickness that corresponds to a positive cloud radiative effect. Comparison of daytime and nighttime observations suggests that anvil thinning proceeds more rapidly at night, when net radiative cooling promotes the sinking of cloud top. It is hypothesized that the properties of aged anvil clouds and their susceptibility to radiative destabilization are shaped by the time of day at which the cloud was detrained. These results underscore the importance of small-scale processes in determining the radiative effect of tropical convection.