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The influence of weather patterns on human migration, both within and across borders, is theoretically ambiguous, and empirical estimates thereof vary widely, sometimes to the point of contradiction. Using a combination of census data, weather stations and satellite measurements, we estimate how weather patterns affect migration differentially across administrative units, climate zones, and demographic characteristics of migrants. To avoid overfitting, we complement traditionally-used causal inference methods with out-of-sample evaluation of model predictive performance. We find that, after controlling for local socioeconomic conditions and trends, within-country migration can be predicted by weather patterns alone. Yet this predictive performance grows substantially when weather effects are allowed to differ by age, and education of the migrant. Dry conditions increase within country migration rates, with a relatively greater effect for younger and less-educated people in temperate and dry, hot climate regions. Analysis of cross-border migration rates, however, indicates that weather stress increases international migration of more educated and older individuals and decreases cross-border movement for others. Collectively, our results highlight distinctions between who chooses to and has the means to migrate in response weather variations, and who does not. Therefore, these findings highlight the key value of detailed location- and individual-level information for purposes of identifying heterogeneous mobility responses, and suggest that out-of-sample evaluation methods can help separate estimates of existing complexity in the weather-migration relationship from spurious heterogeneity.