We deposited face-centered cubic (FCC) Co films on glass substrates by sputtering. From Auger-depth profile analysis, we found that there is one CoO layer, about 13 Å thick, lying on the top surface of the Co film, and another CoO layer, about 37 Å thick, lying within the Co/glass interface. At room temperature, the thin CoO film is supposed to be paramagnetic. However, because of the proximity effect between CoO and Co, the CoO layer may become ferromagnetic, with saturation magnetization Mo. By fitting the saturation magnetization (Ms) data of the whole Co/CoO film as a function of (1/tf), where tf is the Co thickness, we can prove that the last conjecture is correct, and the Mo of the CoO layer is indeed not zero. Both the tf dependence of the magnetostriction constant (λs) and the tf dependence of the coercive field (Hc) show a two-region characteristic. The dividing line for the former quantity is at tf = 88 Å, and for the latter it is at tf = 120 Å. When crossing such a dividing line, there is a discontinuous jump in λs (or Hc). These phenomena occur because the lattice-strain and magnetoelastic effects within the CoO layer dominate the λs and the Hc behavior in ultra-thin (tf < 88 Å) Co films. In this region, the roughness-to-thickness ratio (Sq/tf) may also affect λs. Finally, there seems to be no connection between the grain size (D) and Hc.