Use the operators directly with cell references, and calculate the start date inside the criteria string.
Correct version:
=SUMIFS(B:B, A:A, "<="&C1, A:A, ">"&(C1-7))
If you prefer inclusive of both endpoints:
=SUMIFS(B:B, A:A, "<="&C1, A:A, ">="&(C1-7))
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hth
Marcin