Theory recently predicted that the strength of spin-orbit coupling in bilayer graphene, touching on one side a transition metal dichalcogenide layer such as WSe, can be tuned easily by moderate gate voltages. Here, the authors show in both theory and experiment that, while spin-orbit splitting of the band structure is a monotonic function of the applied electric field, the visibility of weak antilocalization, a measure of the spin-orbit coupling strength, follows a largely opposite, and nonmonotonic trend.