Silicate mineral weathering is a scalable strategy for capture and storage of CO2, but its potential has been limited by its slow rate. Bacteria can accelerate mineral weathering by secretion of siderophores, molecules that solubilize iron released from the mineral that would otherwise passivate the mineral surface. Here, we present an experimental and theoretical model for continuous weathering of the mineral olivine in the presence of the marine bacterium Alteromonas macleodii. Through coupled biological and geochemical measurements, we demonstrated that native genetic regulation precludes continuous siderophore production in industrially relevant conditions. To overcome this limitation, we engineered A. macleodii to enhance production of siderophores. Engineered cells conferred a >150% increase in the rate of olivine dissolution and sustained enhanced weathering for >2 weeks. This finding serves as proof of concept that genetic engineering can overcome natural physiological limitations and may enable large scale biological weathering. Broadly, our model will inform the design and implementation of biological catalysts and reactors for industrial mineral weathering.