  The axial $U(1)$ symmetry in the high-temperature phase is investigated with
$N_f = 2$ lattice QCD simulations. The gauge ensembles are generated with
M\"obius domain-wall fermions, and the overlap/domain-wall reweighting is
applied. We find that the $U(1)_A$ susceptibility evaluated from the spectrum
of overlap-Dirac eigenvalues is strongly suppressed in the chiral limit. We
also study its volume dependence.
