Tamarkin provided a method to prove non-displaceability of subsets of
cotangent bundles with respect to Hamiltonian isotopies using the
microlocal sheaf theory. For a sheaf on the product of a manifold and the
real line, a closed set named as the reduced microsupport is determined as
a subset of the cotangent bundle of the manifold, and non-displaceability
of the reduced microsupports follows from properties of the sheaves. On
the other hand, Entov-Polterovich introduced the concepts of heaviness and
superheaviness as more precise concepts leading to non-displaceability.

In this talk, I provide a general sufficient condition for the reduced
microsupport to be heavy or superheavy. As examples, I show the
superheaviness of certain fibers of classical integrable systems such as
the spherical pendulum and the Lagrange top. This gives an alternative
proof of a result due to Kawasaki-Orita.