Can this be done with the existing Reports or added as a new feature. Basically I need a report that will show the total amount of time I spent on each task broken down per week.
I would have a date range of 1 month and then get the task time breakdown/week.
You may want to give the project activity report a look. If you run that report and select "by task" in the summary drop down the bottom half of the report will include each task that was worked on during the time period selected. The report will not group by week as described above but it is fairly close .
The project activity report with "by task" selected in the summary drop down does show the financial value of the work performed for the time period that the report was run. For example:
If you need to see payments, expenses/fees, and the total value of work navigating to the project dashboard page for the project might be worth a look.