  We classify the finite dimensional semi-weight representations of the reduced
stated skein algebras at odd roots of unity of connected marked surfaces which
either have a boundary component with at least two boundary edges or which do
not have any unmarked boundary component. We deduce computations of the
PI-degrees and Azumaya loci of unreduced stated skein algebras of essential
surfaces having at most one boundary arc per boundary component and of the
unrestricted quantum moduli algebras of lattice gauge field theory.
