We use a multilevel approach to investigate whether a general and robust relationship between weather shocks and (internal and international) migration intentions can be uncovered in Western African countries. We combine individual survey data with measures of localized weather shocks for thirteen countries over the 2008-2016 period. A meta-analysis on results from about 51,000 regressions is conducted to identify the specification of weather anomalies that maximizes the goodness of fit of our empirical model. We then use this best specification to document heterogeneous mobility responses to weather shocks. We find that variability in SPEI/rainfall is associated with changing intentions to move locally or internationally in a few countries only. However, the significance, sign and magnitude of the effect are far from being robust and consistent across countries. These differences might be due to imperfections in the data or to differences in long-term climate conditions and adaptation capabilities. They may also suggest that credit constraints are internalized differently in different settings, or that moving internally is not a relevant option as weather conditions are spatially correlated while moving abroad is an option of last resort. Although our multilevel approach allows us to connect migration intentions with the timing and spatial dimension of weather shocks, identifying a common specification that governs weather-driven mobility decisions is a very difficult, if not impossible, task, even for countries belonging to the same region. Our findings also call for extreme caution before generalizing results from specific case-studies.