  Entov and Polterovich considered the concept of heaviness and superheaviness
by the Oh-Schwarz spectral invariants. The Oh-Schwarz spectral invariants are
defined in terms of the Hamiltonian Floer theory. In this paper, we define
heaviness and superheaviness by spectral invariants defined in terms of the
Lagrangian Floer theory and provide their applications. As one of them, we
define a relative symplectic capacity which measures the existence of
Hamiltonian chord between two disjoint Lagrangian submanifolds and provide an
upper bound of it in a special case. We also provide applications to
non-degeneracy of spectral norms, a relative energy capacity inequality,
fragmentation norm and non-displaceability.
