  Experimentally it is possible to manipulate the director in a (chiral)
smectic-$A$ elastomer using an electric field. This suggests that the director
is not necessarily locked to the layer normal, as described in earlier papers
that extended rubber elasticity theory to smectics. Here, we consider the case
that the director is weakly anchored to the layer normal assuming that there is
a free energy penalty associated with relative tilt between the two. We use a
recently developed weak-anchoring generalization of rubber elastic approaches
to smectic elastomers and study shearing in the plane of the layers, stretching
in the plane of the layers, and compression and elongation parallel to the
layer normal. We calculate, inter alia, the engineering stress and the tilt
angle between director and layer normal as functions of the applied
deformation. For the latter three deformations, our results predict the
existence of an instability towards the development of shear accompanied by
smectic-$C$-like order.
