  Let $G$ be a branch group acting by automorphisms on a rooted tree $T$.
Stabilizers of infinite rays in $T$ are examples of weakly maximal subgroups of
$G$ (subgroups that are maximal among subgroups of infinite index), but in
general they are not the only examples.
  In this note we describe two families of weakly maximal subgroups of branch
groups. We show that, for the first Grigorchuk group as well as for the torsion
GGS groups, every weakly maximal subgroup belongs to one of these families. The
first family is a generalization of stabilizers of rays, while the second one
consists of weakly maximal subgroups with a block structure. We obtain
different equivalent characterizations of these families in terms of finite
generation, the existence of a trivial rigid stabilizer, the number of
orbit-closures for the action on the boundary of the tree or by the means of
sections.
