  For constant mean curvature surfaces of class $C^2$ immersed inside Sasakian
sub-Riemannian 3-manifolds we obtain a formula for the second derivative of the
area which involves horizontal analytical terms, the Webster scalar curvature
of the ambient manifold, and the extrinsic shape of the surface. Then we prove
classification results for complete surfaces with empty singular set which are
stable, i.e., second order minima of the area under a volume constraint, inside
the 3-dimensional sub-Riemannian space forms. In the first Heisenberg group we
show that such a surface is a vertical plane. In the sub-Riemannian hyperbolic
3-space we give an upper bound for the mean curvature of such surfaces, and we
characterize the horocylinders as the only ones with squared mean curvature 1.
Finally we deduce that any complete surface with empty singular set in the
sub-Riemannian 3-sphere is unstable.
