How DFT-D3 affects 3-d vs. layered structures

I’ve run into a peculiar behavior in a D3 vdW corrected DFT calculation, and I was wondering if anyone had any thoughts about it.

The basic observation is that with plain PBE a layered structure with distinctly large distances between layers was essentially degenerate with a fully 3-d connected structure. When I turned on D3 vdW contributions, the layered structure became substantially higher in relative energy compared to the 3-d structure, while the inter-layer spacing became smaller (upon relaxation).

I found this weird, based on an admittedly naive intuition that the vdW correction could only enhance inter-layer attraction (like the LJ 1/r^6 terms). But that would presumably have led to the layered structure having lower energy, and even lower with relaxation. The fact that the layers come closer with D3 relaxation is consistent with this idea of increased attraction, but the 3-d structure’s energy goes down (when adding D3) even more than the layered structure, so they end up with the layered structure having higher energy.

Basically, I was surprised that the D3 correction lowers the energy of the 3-d bonded structure a lot - it just feels like the wrong physics for the dispersion interaction. Does anyone know of a way to think about the D3 correction that explains this behavior? Should I be worried about applying it to a system which has both layered and 3-d bonded structures?