  We present new multi-frequency ALMA continuum observations of the massive
[$\log_{10}(M_\star/M_\odot) = 10.3_{-0.2}^{+0.1}$], UV-luminous
[$M_\mathrm{UV} = -21.7 \pm 0.2$] $z=7.31$ galaxy REBELS-25 in Bands 3, 4, 5,
and 9. Combining the new observations with previously-taken data in Bands 6 and
8, we cover the dust continuum emission of the galaxy in six distinct bands --
spanning rest-frame $50-350\,\mu$m -- enabling simultaneous constraints on its
dust mass ($M_\mathrm{dust}$), temperature ($T_\mathrm{dust}$) and emissivity
index ($\beta_\mathrm{IR}$) via modified blackbody fitting. Given a fiducial
model of optically thin emission, we infer a cold dust temperature of
$T_\mathrm{dust} = 32_{-6}^{+9}\,$K and a high dust mass of
$\log_{10}(M_\mathrm{dust}/M_\odot) = 8.2_{-0.4}^{+0.6}$, and moderately
optically thick dust does not significantly alter these estimates. If we assume
dust production is solely through supernovae (SNe), the inferred dust yield
would be high, $y = 0.7_{-0.4}^{+2.3}\,M_\odot$ per SN. Consequently, we argue
grain growth in the interstellar medium of REBELS-25 also contributes to its
dust build-up. This is supported by the steep dust emissivity index
$\beta_\mathrm{IR} = 2.5 \pm 0.4$ we measure for REBELS-25, as well as by its
high stellar mass, dense interstellar medium, and metal-rich nature. Our
results suggest that constraining the dust emissivity indices of high-redshift
galaxies is important not only to mitigate systematic uncertainties in their
dust masses and obscured star formation rates, but also to assess if dust
properties evolve across cosmic time. We present an efficient observing setup
to do so with ALMA, combining observations of the peak and Rayleigh-Jeans tail
of the dust emission.
