The global overlap between poverty and climate damages raises the question of whether poverty amplifies vulnerability to weather shocks. Combining high-resolution satellite measures of droughts and floods with household panel data from Bangladesh, we study settings where some households are lifted out of poverty through BRAC's graduation program. In control areas, the poorest households experience the largest consumption losses following unpredictable weather shocks; in treated areas, they do not. The difference arises because, in control areas, monopsonistic landlords can pass weather---induced income shocks onto casual laborers---the poor's only employment option. In treated areas, by contrast, program beneficiaries diversify their labor supply, increasing its elasticity and limiting landlords' ability to shift shocks onto workers.