I suppose a weekly report depends on the size of your business but from my personal point of view, a weekly report does seem quite excessive...
I think its harder to monitor performances/results on a weekly basis then it is, say on a monthly basis.. What I mean is, by having weekly meetings etc, by the time the next one comes around have you actually had time to action or monitor the previous weeks points?? Especially if you have other things to do as well?
Monthly (or even fortnightly), however, gives you ample time to monitor, action and find new areas of perhaps concern etc.
If anything does need your attention in between meetings/reports etc, then yes, you look into it and put in place arrangements to control it / report it etc as would be expected of you.
PS: Keith beat me to it - some weeks you may even struggle to put anything or noteworthy into a report..