Many project managers and customers find it difficult to get a good overview of status and achievements when having to look at the hours spent on individual days, especially when there are many people on the project. Weekly reporting would help this enormously.
The basic reporting requirement should be easily fulfilled, since you already have a function to tally up hours by week (displayed in timesheet entry). All you need is an additional sorting / grouping option in the report definition. So in addition to "By Date", add "By Week".

To make this even more powerful, if each user had a Simple text box below the timesheet entry week grid named "Summary Notes for week", he could enter his main focus or main achievements for the week. Almost like a standup note for the week instead of the day. In addition to being a useful reminder to the end user (private note), these notes (public notes) could be optionally displayed when running the week report.