  ALMA surveys of nearby star-forming regions have shown that the dust mass in
the disk is correlated with the stellar mass, but with a large scatter. This
scatter could indicate either different evolutionary paths of disks or
different initial conditions within a single cluster. We present ALMA Cycle 3
follow-up observations for 14 Class II disks that were low S/N detections or
non-detections in our Cycle 2 survey of the $\sim 2$ Myr-old Chamaeleon I
star-forming region. With 5 times better sensitivity, we detect millimeter dust
continuum emission from six more sources and increase the detection rate to
94\% (51/54) for Chamaeleon I disks around stars earlier than M3. The
stellar-disk mass scaling relation reported in \citet{pascucci2016} is
confirmed with these updated measurements. Faint outliers in the
$F_{mm}$--$M_*$ plane include three non-detections (CHXR71, CHXR30A, and T54)
with dust mass upper limits of 0.2 M$_\oplus$ and three very faint disks
(CHXR20, ISO91, and T51) with dust masses $\sim 0.5$ M$_\oplus$. By
investigating the SED morphology, accretion property and stellar multiplicity,
we suggest for the three millimeter non-detections that tidal interaction by a
close companion ($<$100 AU) and internal photoevaporation may play a role in
hastening the overall disk evolution. The presence of a disk around only the
secondary star in a binary system may explain the observed stellar SEDs and low
disk masses for some systems.
