We develop NSk--Gravity, the gravitational module of the NSk/ψ program, in which gravity emerges as a stabilising drift on a partition lattice rather than as a separately postulated field. The core mechanism is purely finite and graph-theoretic: mass is transported towards higher values of the existence density P, a field defined by cellular averaging over a neighbourhood graph. The module is organised into layers — PRE-PURE (partition lattice and coarse-graining), PURE (canonical gravitational field g = −∇_G P), CORE-A (stabilising drift operator and monotonicity theorem), CORE-B (self-consistent Poisson variant), and CORE-C (admissibility gate and multiscale certificate) — forming a self-contained deductive core on which downstream modules can build without returning to realisation layers. For the canonical H1 realisation on a helical q3D torus, we derive a full Newton theorem-package: the Green's function asymptotics 1/(4πr), the inverse-square law after source normalisation, and the effective Newton constant G_NSk. A weak-field Einsteinian bridge (EXT) yields gravitational time dilation, frequency redshift, and the metric coefficient g_00, with proofs conditional on contracts imported from NSk--Einstein. General relativity is explicitly separated into the EXT layer and is not part of the deductive core.