The trade-off between yield and quality, a major problem for the production of fleshy fruits, involves fruit expansive growth and sugar metabolism. Here we developed an integrative model by coupling a biophysical model of fleshy fruit growth processes, including water and carbon fluxes and organ expansion, with an enzyme-based kinetic model of sugar metabolism to better understand the interactions between these two processes. The integrative model was initially tested on tomato fruit, a model system for fleshy fruit. The integrative model simulated well the biomass and major carbon metabolites of tomato fruit developing under optimal or stress conditions. The model also performed robustly when simulating the fruit size and sugar concentrations of different tomato genotypes including wild species. The validated model was used to explore ways of uncoupling the size-sweetness trade-off in fruit. Model-based virtual experiments suggested that larger sweeter tomatoes could be obtained by simultaneously manipulating certain biophysical factors and transmembrane transports. The integrative fleshy fruit model provides a promising tool to facilitate targeted bioengineering and breeding of tomatoes and other fruits.