Bacteria evolve resistance to antibiotics by a multitude of mechanisms. A central, yet unsolved question is how resistance evolution affects cell growth at different drug levels. Here, we develop a fitness model that predicts growth rates of common resistance mutants from their effects on cell metabolism. The model maps metabolic effects of resistance mutations in drug-free environments and under drug challenge; the resulting fitness trade-off defines a Pareto surface of resistance evolution. We predict evolutionary trajectories of growth rates and resistance levels, which characterize Pareto resistance mutations emerging at different drug dosages. We also predict the prevalent resistance mechanism depending on drug and nutrient levels: low-dosage drug defence is mounted by regulation, evolution of distinct metabolic sectors sets in at successive threshold dosages. Evolutionary resistance mechanisms include membrane permeability changes and drug target mutations. These predictions are confirmed by empirical growth inhibition curves and genomic data of Escherichia coli populations. Our results show that resistance evolution, by coupling major metabolic pathways, is strongly intertwined with systems biology and ecology of microbial populations.