Not out of the box. It has monthly and yearly plans built in. You could add it in though by creating some weekly functionality.
The user can pause subscriptions though, so that part would work out of the box. If they pause it, it will allow them to continue to use the app up until the end of their current subscription (like if I pay on Monday for a weekly plan it will be good through Sunday even if I pause on Tuesday). Then they can resume whenever they want and it will start charging again.