Who's the Leader, Anyway?
It's not necessary for the same person to always lead the group. There is much value in leadership rotating around the members of the group. Perhaps different people could lead different parts of the meeting?
However leadership is exercised there' is a lot to be said for allowing the whole group to assess how the meetings are going, and to plan for the future. Not every time you meet but from time to time. It means that responsibility for the group will be seen to rest with everybody not just with one or two for whom it can easily become a burden. It also means that it is less likely that any individual's needs will be forgotten.
If one person remains recognisably the leader, and there may be such a person even if the leadership of meetings is shared, then who supports them? Who do they talk to about how things are going?
Beware of members who seek to hijack the group: to dominate it or to impose their own personal agenda upon it.