Living cells react to changes in growth conditions by re-shaping their proteome. This accounts for different stress-response strategies, both specific (i.e., aimed at increasing the availability of stress-mitigating proteins) and systemic (such as large-scale changes in the use of metabolic pathways aimed at a more efficient exploitation of resources). Proteome re-allocation can, however, imply significant biosynthetic costs. Whether and how such costs impact the growth performance are largely open problems. Focusing on carbon-limited E. coli growth, we integrate genome-scale modeling and proteomic data to address these questions at quantitative level. After deriving a simple formula linking growth rate, carbon intake, and biosynthetic costs, we show that optimal growth results from the tradeoff between yield maximization and protein burden minimization. Empirical data confirm that E. coli growth is indeed close to Pareto-optimal over a broad range of growth rates. Moreover, we establish that, while most of the intaken carbon is diverted into biomass precursors, the efficiency of ATP synthesis is the key driver of the yield-cost tradeoff. These findings provide a quantitative perspective on carbon overflow, the origin of growth laws and the multidimensional optimality of E. coli metabolism.