  Let $G$ be a finitely generated regular branch group acting by automorphisms
on a regular rooted tree $T$. It is well-known that stabilizers of infinite
rays in $T$ (aka parabolic subgroups) are weakly maximal subgroups in $G$, that
is, maximal among subgroups of infinite index. We show that, given a finite
subgroup $Q\leq G$, $G$ possesses uncountably many automorphism equivalence
classes of weakly maximal subgroups containing $Q$. In particular, for
Grigorchuk-Gupta-Sidki type groups this implies that they have uncountably many
automorphism equivalence classes of weakly maximal subgroups that are not
parabolic.
