The low-temperature magnetic susceptibility of normal and superfluid 3He confined between mylar foils spaced 4.0 mu m apart shows a large and field-dependent enhancement over the bulk Fermi liquid magnitude. The excess susceptibility disappears when the liquid is doped with 0.5% 4He. The reason for the excess is unknown. The authors also studied the proton resonance of the mylar substrate and obtained spin polarizations large enough to permit the direct observation of double spin-flip RF absorption.