You will get the answer when you consider what it is that you wish to achieve by having a weekly meeting. Whatever your answer, it is important that you follow a preset format, including the time limits for the meeting. You can do this by having an agenda, which is sent out to all that will be present in the meeting.
Below is an example of an agenda:
A meeting is to be held on dd/mm/year. The venue will be XXXXXXXXXX. The meeting will commence at (time) and is expected to last for xx hour(s).
The topics for discussion are:
1) xxxxxxxxxx
2) xxxxxxx
etc.
The final topic should always be "Any other business." However, please remember that you should not include any topics that are best discussed one-on-one. All topics should be of interest to all; this will ensure full participation.
Finally, end the meeting with a date, time, and venue for the next meeting. Start the next meeting with a short review of the actions agreed upon at the previous meeting.
Hope the above helps.
Regards, Harsh