  Hypergraphs are a generalization of graphs in which edges can connect any
number of vertices. They allow the modeling of complex networks with
higher-order interactions, and their spectral theory studies the qualitative
properties that can be inferred from the spectrum, i.e. the multiset of the
eigenvalues, of an operator associated to a hypergraph. It is expected that a
small perturbation of a hypergraph, such as the removal of a few vertices or
edges, does not lead to a major change of the eigenvalues. In particular, it is
expected that the eigenvalues of the original hypergraph interlace the
eigenvalues of the perturbed hypergraph. Here we work on hypergraphs where, in
addition, each vertex--edge incidence is given a real number, and we prove
interlacing results for the adjacency matrix, the Kirchoff Laplacian and the
normalized Laplacian. Tightness of the inequalities is also shown.
