  Weakly stable constant mean curvature (CMC) hypersurfaces are stable critical
points of the area functional with respect to volume preserving deformations.
We establish a pointwise curvature estimate (in the non-singular dimensions)
and a sheeting theorem (in all dimensions) for weakly stable CMC hypersurfaces,
giving an effective version of the compactness theorem for weakly stable CMC
hypersurfaces established in the recent work of the first and third-named
authors. Our results generalize the curvature estimate and the sheeting theorem
proven respectively by Schoen--Simon--Yau and Schoen--Simon for strongly stable
hypersurfaces.
