We report evidence for an excited molecular anionic resonance in a model system, bilayer C6F6 adsorbed on Cu(111). This resonance is dispersed parallel to the surface, with an effective electron mass of 1.5 m(e). Both the energetic position and the dispersion of this molecular resonance depend on the strength of molecule-surface interaction, which is weakened by the preadsorption of atomic H. With increasing coverage of preadsorbed H from theta = 0 to 0.34 monolayer (ML), the position of the molecular resonance increases from 2.99 to 3.22 eV above the Fermi level. This is accompanied by a decrease in effective electron mass from 1.5 me on clean Cu(111) to 0.55 m(e) on 0.34 ML H-covered Cu(111). We attribute this to the improved molecule-molecule interaction as the molecule-surface interaction weakens.