High conductivity in the off-state and low field-effect mobility compared to bulk properties is widely observed in the p-type thin-film transistors of Cu2O, especially when processed at moderate temperature. This work presents results from in situ conductance measurements at thicknesses from sub-nm to around 250 nm with parallel X-ray photoelectron spectroscopy. An enhanced conductivity at low thickness is explained by the occurrence of Cu(II), which is segregated in the grain boundary and locally causes a conductivity similar to CuO, although the surface of the thick film has Cu2O stoichiometry. Since grains grow with an increasing film thickness, the effect of an apparent oxygen excess is most pronounced in vicinity to the substrate interface. Electrical properties of Cu2O grains are at least partially short-circuited by this effect. The study focuses on properties inherent to copper oxide, although interface effects cannot be ruled out. This non-destructive, bottom-up analysis reveals phenomena which are commonly not observable after device fabrication, but clearly dominate electrical properties of polycrystalline thin films.