  We provide two candidates for symplectic Weiss calculus based on two
different, but closely related, collections of groups. In the case of the
non-compact symplectic groups, i.e., automorphism groups of vector spaces with
symplectic forms, we show that the calculus deformation retracts onto unitary
calculus as a corollary of the fact that Weiss calculus only depends on the
homotopy type of the groupoid core of the diagram category. In the case of the
compact symplectic groups, i.e., automorphism groups of quaternion vector
spaces, we provide a comparison with the other known versions of Weiss calculus
analogous to the comparisons of calculi of the second named author, and
classify certain stably trivial quaternion vector bundles over finite cell
complexes in a range, using elementary results on convergence of Weiss calculi.
