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One way of doing this is by duplicating the data source, creating a calculated field referencing one week in the future, and having the relationship between the two data sources be the week difference field (Kind of Confusing to explain so I will try and expand).
1. Right Click on Data Source and Duplicate:
2. Create Calculated Field on Primary Data Source: (Essentially just the As of Date formatted)
DATETRUNC('day',DATEADD('day',0,[As at Date]))
3. Create Calculated Field on Second Data Source with same name:
DATETRUNC('day',DATEADD('day',7,[As at Date]))
4. Unlink [As of Date] Dimension and Link on [As at Date1]
5. Create the Percent Difference Calculation on the Primary Data Source:
(avg([Value])-avg([Sheet1 (Test Data Dates) (copy)].[Value]))/avg([Sheet1 (Test Data Dates) (copy)].[Value])
6. Change your Date Filter to a single value
7. Add your Percent to the Detail, Format as a percent (Before you bring it to the Title), and add it to the Title
This will only work if your [As at Date] is 7 days apart. It was for your example (For 12/28 and 12/21) so I figured it would work. If they have a different date range there are other ways we could do it but I thought this might get you started.
Sorry for the late reply - thanks alot!