[The Might]

I thought of the Stoors as well, and since at one point the Hobbits were still one folk it could be that all Hobbits used at one point a matriarchal system, and that afterwards those in the Shire changed this habit and adopted new ones perhaps similar to those in Arnor

In the First Age we also have examples of people being led by a woman - the folk of Haleth or Haladin, though it is important in my opinion to keep in mind that she only claimed this title after her brother and father had been killed by Orcs in Thargelion
Still, the fact that her people followed her and did not look for another person to rule them, shows that these Men war open minded, unlike those in later ages where it is visible the role of women in society had decreased a lot