  We study the weighted spectrum and vanishing cohomology for several classes
of isolated hypersurface singularities, and how they contribute to the limiting
mixed Hodge structure of a smoothing. Applications are given to several types
of singularities arising in KSBA and GIT compactifications and mirror symmetry,
including nodes on odd-dimensional hypersurfaces, $k$-log-canonical and
$k$-rational singularities, and singularities with Calabi-Yau tail.
