  The absolute values and temperature, T, dependence of the in-plane magnetic
penetration depth, $\lambda_{ab}$, of La_{2-x}Sr_xCuO_4 and
HgBa_2CuO_{4+\delta} have been measured as a function of carrier concentration.
We find that the superfluid density, $\rho_s$, changes substantially and
systematically with doping. The values of $\rho_{s}(0)$ are closely linked to
the available low energy spectral weight as determined by the electronic
entropy just above T_c and the initial slope of $\rho_{s}(T)/\rho_{s}(0)$
increases rapidly with carrier concentration. The results are discussed in the
context of a possible relationship between $\rho_s$ and the normal-state (or
pseudo) energy gap.
