Spin-orbit coupling in two-dimensional materials gives rise to a Rashba spin splitting when inversion and mirror symmetries are broken, yet its microscopic origin and quantitative characterization in transition metal dichalcogenides remain incomplete. Using first-principles calculations, we investigate monolayer M X 2 transition metal dichalcogenides ( M = Mo , W; X = S , Se, Te), and homobilayers lacking inversion and mirror symmetries, exhibiting zero-field Rashba splitting. We determine the field- and momentum-independent Rashba coefficients and intrinsic electric fields of these systems, establishing a direct connection to the Rashba Hamiltonian. Surprisingly, the Rashba effect on the topmost valence band is substantially smaller in bilayers than in monolayers at typical fields. This motivates an analytical microscopic model that identifies the orbital processes responsible for Rashba spin splitting. It confirms that, in bilayers, the effect is governed by the competition between layer-resolved charge deformation and interlayer coupling. To quantify this competition, we introduce the orbital polarization imbalance and orbital polarizability as order parameters and, by combining them with first-principles calculations, identify the dominant microscopic channel responsible for the Rashba splitting.