  We investigate the electronic specific heat of overdoped
BaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ single crystals in the superconducting
state using high-resolution nanocalorimetry. From the measurements, we extract
the doping dependence of the condensation energy, superconducting gap $\Delta$,
and related microscopic parameters. We find that the anomalous scaling of the
specific heat jump $\Delta C \propto T_{\mathrm{c}}^3$, found in many
iron-based superconductors, in this system originates from a
$T_\mathrm{c}$-dependent ratio $\Delta/k_\mathrm{B}T_\mathrm{c}$ in combination
with a doping-dependent density of states $N(\varepsilon_\mathrm{F})$. A clear
enhancement is seen in the effective mass $m^{*}$ as the composition approaches
the value that has been associated with a quantum critical point at optimum
doping. However, a simultaneous increase in the superconducting carrier
concentration $n_\mathrm{s}$ maintains the superfluid density, yielding an
apparent penetration depth $\lambda$ that decreases with increasing
$T_\mathrm{c}$ without sharp divergence at the quantum critical point. Uemura
scaling indicates that $T_\mathrm{c}$ is governed by the Fermi temperature
$T_\mathrm{F}$ for this multi-band system.
