The complex relationship between climate shocks, migration, and adaptation hampers a rigorous understanding of the heterogeneous mobility outcomes of farm households exposed to climate risk. To unpack this heterogeneity, the analysis combines longitudinal multi-topic household survey data from Nigeria with a causal machine learning approach, tailored to a conceptual framework bridging economic migration theory and the poverty traps literature. The results show that pre-shock asset levels, in situ adaptive capacity, and cumulative shock exposure drive not just the magnitude but also the sign of the impact of agriculture-relevant weather anomalies on the mobility outcomes of farming households. While local adaptation acts as a substitute for migration, the roles played by wealth constraints and repeated shock exposure suggest the presence of climate-induced immobility traps.