The observation of quantized Chern numbers in twisted transition metal dichalcogenide (TMD) homobilayers, including 3.7° twisted MoTe₂ and 1.23° twisted WSe2, represents a landmark breakthrough in moiré physics. A striking and unresolved paradox to emerge from these studies is the unexpected opposite sign of the measured Chern numbers between the two systems, a discrepancy that strongly hints at a twist-angle-dependent reversal of the Chern number sign. Despite this compelling implication, direct experimental validation of such a sign reversal within a single twisted TMD homobilayer system is still elusive. Here, we report the first experimental demonstration that the Chern numbers of the moiré frontier bands undergo sign reversal at a critical twist angle ~1.42° in twisted WSe2 bilayers (tWSe2). Using scanning tunnelling microscopy and spectroscopy, we directly measure layer-pseudospin skyrmion textures of tWSe2 and our results reveal that tWSe2 in the vicinity of the 1.42° exhibits a twist-angle-dependent layer-pseudospin polarization, an effect that serves as the fundamental origin of the observed Chern number sign reversal.