  We present a combined, homogenized analysis of archival Submillimeter Array
(SMA) and Atacama Large Millimeter/submillimeter Array (ALMA) observations of
the spatially resolved 340 GHz (870 $\mu$m) continuum emission from 105 nearby
protoplanetary disks. Building on the previous SMA survey, we infer surface
brightness profiles using a simple model of the observed visibilities to derive
the luminosities ($L_{\rm mm}$) and effective sizes ($R_{\rm eff}$) of the
continuum emission. With this sample, we confirm the shapes, normalizations,
and dispersions for the strong correlations between $L_{\rm mm}$, $M_\ast$ (or
$L_\ast$), and $\dot{M}_\ast$ found in previous studies. We also verify the
continuum size--luminosity relation determined from the SMA survey alone
(extending to an order of magnitude lower $L_{\rm mm}$), demonstrating that the
amount of emission scales linearly with the emitting surface area. Moreover, we
identify new, although weaker, relationships between $R_{\rm eff}$ and the host
and accretion properties, such that disks are larger around more massive hosts
with higher accretion rates. We explore these inter-related demographic
properties with some highly simplified approximations. These multi-dimensional
relationships can be explained if the emission is optically thick with a
filling factor of $\sim$0.3, or if the emission is optically thin and disks
have roughly the same optical depth profile shapes and normalizations
independent of host properties. In both scenarios, we require the dust disk
sizes to have a slightly sub-linear relationship with the host mass and a
non-negligible dispersion ($\sim$0.2 dex at a given $M_\ast$).
