Weakly maximal subgroups in regular branch groups

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≤GQ≤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.