  We prove that statistically stationary martingale solutions of the 3D
Navier-Stokes equations on $\mathbb{T}^3$ subjected to white-in-time
(colored-in-space) forcing satisfy the Kolmogorov 4/5 law (in an averaged sense
and over a suitable inertial range) using only the assumption that the kinetic
energy is $o(\nu^{-1})$ as $\nu \rightarrow 0$ (where $\nu$ is the inverse
Reynolds number). This plays the role of a weak anomalous dissipation. No
energy balance or additional regularity is assumed (aside from that satisfied
by all martingale solutions from the energy inequality). If the force is
statistically homogeneous, then any homogeneous martingale solution satisfies
the spherically averaged 4/5 law pointwise in space. An additional hypothesis
of approximate isotropy in the inertial range gives the traditional version of
the Kolmogorov law. We demonstrate a necessary condition by proving that energy
balance and an additional quantitative regularity estimate as $\nu \rightarrow
0$ imply that the 4/5 law (or any similar scaling law) cannot hold.
