We present local probe tunneling spectroscopy of Bi2Sr2CaCu2O8+delta single crystals for different oxygen concentrations, from optimally doped (T-c = 92.2 K) to highly overdoped (T-c = 56.0 K) phases. With increasing oxygen overdoping, the superconducting gap (Delta(p)) is reduced and the dip structure beyond Delta(p) at negative sample bias(1) shifts reward the Fermi energy. Apart from the shift in energy of these features, the generic shape of the tunneling spectra remains unchanged. The gap roughly scales with T-c, and 2 Delta(p)/k(B)T(c) stays large even in the highly overdoped phase. We also present preliminary results on the temperature dependence of the tunneling spectra. They are consistent with a gap that is largely independent on temperature up to the vicinity of T-c.