Many songbirds alternate migratory flights with stopovers to rest and refuel. Understanding the effects of weather on the timing of take-offs from stopover sites is key to mitigating human-wildlife conflicts during peak migration. We leveraged weather radar observations covering the contiguous United States to analyze how responses to weather vary across space and time. The ecological interpretation of a process-guided deep learning model reveals that local take-off is driven by wind, followed by temperature and humidity, through distinct interaction effects. In spring, winds generally suppress take-offs except in regions with rare supportive winds or after periods with unfavorable winds. In fall, migrants show greater flexibility, dynamically adjusting their tolerance for unfavorable winds depending on regional climatology and preceding conditions. Our findings highlight the flexibility of migratory birds in adapting to changing weather conditions, emphasizing the need for advanced models to capture these context-dependent behaviors.