For a compact subset K of a closed symplectic manifold, Entov-Polterovich introduced the notion of (super)heaviness, which reveals surprising symplectic rigidity. When K is a Lagrangian submanifold, there is a well-established criterion for its heaviness, by using closed-open maps. We will discuss an equivalence between the heaviness and the non-vanishing of the relative symplectic cohomology, for a general compact set K . Joint with C.Y.Mak and U.Varolgunes.