I think stores can only get on a limited amount of game night kits (ffg's officially prize support), which limits you if your goal is weekly tournaments. I think they're limited to two or three per store, and you have to be a store to order them. So on weeks where you didn't have a gnk, you'd have to do something like suggested above with the entry fee.
Something we do at one of the stores I play at during the week might work as well. We have a league we play in every week with a $1 entry fee. Every... 3? I think? months, the league ends, and prizes are awarded from the gnk prize pool. The points are awarded for a win, and one for a loss; this way it's better to show up and lose than not show up at all. It's a slower format than a tourney every week, but it makes the limited official prize support stretch further.