  We apply the theory of Weyl structures for parabolic geometries developed by
A. Cap and J. Slovak in to compute, for a quaternionic contact (qc) structure,
the Weyl connection associated to a choice of scale, i.e. to a choice of
Carnot-Carath\'eodory metric in the conformal class. The result of this
computation has applications to the study of the conformal Fefferman space of a
qc manifold. In addition to this application, we are also able to easily
compute a tensorial formula for the qc analog of the Weyl curvature tensor in
conformal geometry and the Chern-Moser tensor in CR geometry. This tensor
agrees with the formula derived via independent methods by S. Ivanov and D.
Vasillev. However, as a result of our derivation of this tensor, its
fundamental properties -- conformal covariance, and that its vanishing is a
sharp obstruction to local flatness of the qc structure -- follow as easy
corollaries from the general parabolic theory.
