  The Compton double-polarization observable $\Sigma_{2z}$ has been measured
for the first time in the $\Delta(1232)$ resonance region using a circularly
polarized photon beam incident on a longitudinally polarized target at the
Mainz Microtron. This paper reports these results, together with the
model-dependent extraction of four proton spin polarizabilities from fits to
additional asymmetry data using dispersion relation and chiral perturbation
theory calculations, with the former resulting in: $\gamma_{E1E1} = -3.18 \pm
0.52$, $\gamma_{M1M1} = 2.98 \pm 0.43$, $\gamma_{E1M2} = -0.44 \pm 0.67$ and
$\gamma_{M1E2} = 1.58 \pm 0.43$, in units of $10^{-4}~\mathrm{fm}^{4}$.
