Microorganisms show some conserved relations between physiological state and environmental conditions. Growth Robustness Reciprocity (GRR) is an intriguing example: genetic and environmental factors that impair microorganism’s vegetative performance (growth rate) enhance their ability to resist abiotic stresses, and vice-versa. Mechanistically, this relationship may be explained by regulatory interactions that determine higher expression of protection mechanisms in response to low growth rates. However, these mechanisms are not conserved. Therefore, the observed GRR must result from convergent evolution. Why does natural selection favor such an outcome? Here, we used mathematical models of optimal resource allocation in an idealized cellular self-replicating system to identify the general evolutionary and physiological principles that may explain why GRR is widespread. These models account for the cell protein components involved in: (i) substrate uptake from environment, (ii) metabolic transformation of substrate to anabolic precursors, (iii) biosynthesis (e.g. ribosomes and lipid synthesizing enzymes), (iv) protein inactivation, representing stress, and (v) stress defenses. The relative fraction of each cell component is optimized by adjusting the proportion of ribosomes engaged in its synthesis so as to maximize the growth rate. We found that optimal resource allocation determines that at high substrate availabilities and low stress intensities stress defenses are not expressed. Under these conditions, stress tolerance ensues from growth-related damage dilution: the higher the substrate availability, the highest the growth rate, the fastest the dilution of damaged proteins by newly synthesized proteins, the highest the stress that can be tolerated until the inactive pool drains all the cell resources necessary for growth. In turn, under low substrate availability or high stress lower growth rates can be attained, and thus growth-related damage dilution is less effective. Under these conditions, growth is maximized when stress defenses are expressed, and their expression is higher the lower the nutrient concentrations and biosynthetic efficiency. Our optimality models reproduce the negative correlation between the expression of stress protection and the expression of growth-promoting genes that is observed in microorganisms. As a consequence of this phenomenon, slow-growing but not fast-growing cells are pre-adapted to withstand acute stresses. Overall, these results show that GRR can be explained by the interplay among three general principles. Namely (a) damage and biosynthesis errors that inactivate cellular components are inevitable, (b) faster-growing cells are often selectively favored, (c) growth-associated synthesis of new components dilutes damage, with the consequence that cells in more favorable environments grow fastest when expressing defenses the least.