To create a weekly plan (or bi-weekly for that matter!), you can use the feature Expiring Day Passes.
Don't include any free passes.
Under the volume discount, provide the option to purchase 7 passes (i.e., a week's worth).
Now your member won't be charged until they purchase a pack of day passes. The passes will automatically expire at the end of the 7 days.
You can also choose to turn on the feature that makes your members pay for time passes immediately, which means members are charged at the point of purchase. This would also apply to the purchase of booking passes for resources. You can activate this under Customize » Features » Payments.