Sum formula based on a changing week

[TAG423]

I have a spreadsheet that has the date from Column A to AE (31 days...8/1, 8/2, etc.). Call it Row 1. In Row 2, I have values under each date. I need a formula that sums up by the week. The week is Sunday to Saturday. Each month the starting cell for the formula will change because the dates change. I want to avoid having to change the formula each month.

Any suggestions?

 

[TAG423]

To clarify, I would usually have 5 weeks and 5 separate formulas. Week 1 may be Wed to Sat. Then Sun to Sat for each week after that. Week 1 is short depending on what day the month starts with. But all 5 formulas now have to be changed. I want to eliminate the changing of these formulas.

Thanks.