  We study defect energy levels in hexagonal boron-nitride with varying number
of layers using a fragment many-body $GW$ formalism, taking as examples the
paradigmatic carbon-dimer and $C_BV_N$ defects. We show that a single layer can
be fragmented in polarizable finite-size areas reproducing faithfully the
effect of the dielectric environment, dramatically facilitating the study at
the many-body level of point defects in the dilute limit. The evolution of
defect energy levels from the monolayer to a $n$-layer system due to increased
screening, labeled polarization energies, follow a simple $({\Delta P}/n +
P_{\infty})$ behavior. The coefficients $\Delta P$ and $P_{\infty}$ are found
to be close-to-universal, with opposite signs for holes and electrons,
characterizing mainly the host and the position of the defect (surface or
bulk), but hardly the defect type. Our results rationalize the evolution of
defect energy levels with layers number, allowing to safely extrapolate results
obtained for the monolayer to few-layers, surface or bulk \textit{h}-BN. The
present many-body fragment approach further opens the door to studying
disordered 2D layers.
