The spontaneous expulsion of applied magnetic field, the Meissner effect, is a defining feature of superconductors; in Type-II superconductors above the lower critical field, this screening takes the form of a lattice of magnetic flux vortices. Using implanted spin-1/2 positive muons, one can measure the vortex lattice field distribution through the spin precession and deduce key parameters of the superconducting ground state, and thereby fundamental properties of the superconducting pairing. Muon spin rotation/relaxation (mu SR) experiments have indeed revealed much interesting physics in the underdoped cuprates, where superconductivity is closely related to, or coexistent with, disordered or fluctuating magnetic and charge excitations. Such complications should be absent in overdoped cuprates, which are believed to exhibit conventional Fermi liquid behaviour. These first transverse field (TF)-mu(+) SR experiments on heavily-overdoped single crystals reveal a superfluid density exhibiting a clear inflection point near 0.5T(c), with a striking doping-independent scaling. This reflects hitherto unrecognized physics intrinsic to d-wave vortices, evidently generic to the cuprates, and may offer fundamentally new insights into their still-mysterious superconductivity.