The top-of-atmosphere radiative effect of tropical anvil clouds varies with cloud opacity, and can range from substantially negative to largely positive. Recent climate model assessments have found a decrease in the proportion of thick, or opaque, anvil cloud with warming, resulting in a positive climate feedback. However, the mechanism for this change remains obscure.Lifecycle analysis of deep convective clouds tracked using tobac in the convection-permitting global ICOsahedral Non-hydrostatic model (ICON) shows how anvil area and opacity respond to convection. We find that both properties increase in response to increased convective intensity and convective area, but that their sensitivity to each is not equal. To interpret these results, we independently develop a simple analytical model that links anvil expansion and opacity to convective mass flux (CMF). The model predicts that higher CMF leads to greater anvil expansion, increasing the area of thick anvil cloud. But when anvil opacity also depends on convective intensity, we find a strong, non-linear increase in thick anvil amount in response to increasing CMF, consistent with the response observed in ICON. This implies a strong sensitivity of thick anvil amount to changes in the upper tail of the distribution of CMF and illustrates a possible mechanism by which changes in the distribution of cloud CMF could drive anvil thinning in a warming climate.