We investigate the effect of the Dzyaloshinskii-Moriya interaction (DMI) on domain wall (DW) configurations in W/(Co)FeB/MgO structures with varying ferromagnet (FM) thicknesses. The DW chirality and effective DMI field are evaluated from field-induced DW motion. The results indicate a reversal of DW chirality with the FM thickness irrespective of the FM material (CoFeB or FeB) and the crystallographic phase of W (α or β phase). The observed change in the magnitude of the DMI field is supported by an additional measurement of spin-orbit torque assisted magnetization switching under in-plane magnetic fields. The present findings offer previously unknown insights into the origin of interfacial DMI and indicate the co-existence of multiple factors governing DW chirality in systems with broken inversion symmetry.