Charting the date as continous should result in the desired behavior. Right-click and drag your date onto the Columns shelf, and from the section in green text choose WEEK(date field).
Thanks Eric. I already had my date set to continuous so this doesn't solve it.
Please attach a workbook. The experts in this community are more likely to take interest in your question when they can review your workbook and reply by posting a working solution for you to use. My copy of Tableau isn't current so I won't be able to open the workbook, but that is best as the experts will have better answers than I do.