  Quantum systems are typically characterized by the inherent fluctuation of
their physical observables. Despite this fundamental importance, the
investigation of the fluctuations in interacting quantum systems at finite
temperature continues to pose considerable theoretical and experimental
challenges. Here we report the characterization of atom number fluctuations in
weakly interacting Bose-Einstein condensates. Technical fluctuations are
mitigated through a combination of non-destructive detection and active
stabilization of the cooling sequence. We observe fluctuations reduced by
\SI{27}{\percent} below the canonical expectation for a non-interacting gas,
revealing the microcanonical nature of our system. The peak fluctuations have
near linear scaling with atom number $\Delta N_{0,\mathrm{p}}^2 \propto
N^{1.134}$ in an experimentally accessible transition region outside the
thermodynamic limit. Our experimental results thus set a benchmark for
theoretical calculations under typical experimental conditions.
