Geometric dephasing is distinct from dynamical dephasing processes in that it depends on the trajectory traversed, hence it reverses its sign upon flipping the direction in which the path is traced. Here we study sequences of generalized (weak) measurements that steer a system in a closed trajectory. The readout process is marked by fluctuations, giving rise to dephasing. It comprises a contribution which is invariant under reversal of the sequence ordering, and, in analogy with geometric dephasing, one which flips its sign upon reversal of the winding direction. The latter results in “coherency enhancement”. This asymmetric dephasing diverges at certain protocol parameters, marking a topological transition in the measurement-induced phase factor.