[en] We report scanning tunneling microscopy/spectroscopy (STM/STS) investigations of the band-bending in the vicinity of charged point defects and edges of monolayer MoSe₂ and mono- and trilayer WSe₂ films deposited on graphitized silicon carbide substrates. By tracing the spatial evolution of the structures of the STS spectra, we evaluate the magnitude and the extent of the band-bending to be equal to few hundreds milielectronvolts and several nanometres, respectively. With the aid of a simple electrostatic model, we show that the spatial variation of the Coulomb potential close to the film edges can be well reproduced by taking into account the metallic screening by graphene. Additionally, the analysis of our data for trilayer WSe₂ provides reasonable estimations of its dielectric constant () and of the magnitude of the charge trapped at the defect site (Q  =  +e). (paper)