Using a Molecular Beam Epitaxy deposition technique, c-axis oriented La2−xSrxCuO4±δ thin films (50nm thick) were prepared 001) SrTiO3 substrates. Measurements of the acsheet impedance Z = R + iωLk performed with a two coil mutual inductance technique were used to determine the temperature dependent in-plane penetration depth λab(T) of the layers for various values of their Sr content x. Values of λab(0) deduced from the kinetic inductance Lk(T) and from the vortex pinning activation energy ΔU show an increase of λab(0) with growing carrier density n in the overdoped regime in sharp contrast with the simple London's prediction λab−2(0) ∼ n.