Electron-electron interactions in overdoped Bi-2212 are studied by inelastic light scattering. The optimally to slightly overdoped compounds exhibit two-magnon excitations with a dependence on the incident photon energy typical for doped antiferromagnets. For more overdoped samples, no two-magnon excitation is visible, indicating an antiferromagnetic correlation below twice the lattice parameter. In the same samples, the gap excitation shows a resonance similar to the two-magnon excitation. We interpret our results as a development towards a correlated Fermi liquid when the doping is increased.