  The Robo-AO \textit{Kepler} Planetary Candidate Survey is observing every
\textit{Kepler} planet candidate host star with laser adaptive optics imaging
to search for blended nearby stars, which may be physically associated
companions and/or responsible for transit false positives. We present in this
paper the results of our search for stars nearby 1629 \textit{Kepler} planet
candidate hosts. With survey sensitivity to objects as close as $\sim$0.15" and
magnitude differences $\Delta$m$\le$6, we find 223 stars in the vicinity of 206
target KOIs; 209 of these nearby stars have not previously been imaged in high
resolution. We measure an overall nearby-star probability for \textit{Kepler}
planet candidates of 12.6\%$\pm$0.9\% at separations between 0.15" and 4.0".
Particularly interesting KOI systems are discussed, including 23 stars with
detected companions which host rocky, habitable zone candidates, and five new
candidate planet-hosting quadruple star systems. We explore the broad
correlations between planetary systems and stellar binarity using the combined
dataset of Baranec et al. (2016) and this paper. Our previous 2$\sigma$ result
of a low binary fraction of KOIs hosting close-in giant planets is less
apparent in this larger dataset. We also find a significant correlation between
binary fraction and KOI number, suggesting possible variation between early and
late \textit{Kepler} data releases.

Earth and Planetary Astrophysics