Use defined Tables (Be sure there is no gaps - empty rows or columns - in your datarange. Select any cell in your datarange, and then from Menu Insert > Table. Check 'My table has headers'. OK. The table is created and Design Menu tab is activated. Change the table name in left top in menu bar to meaningful one.)

P.e.
You create a table tDaily on sheet Daily, with header DaySum in column F and DayDate in column A;
On another sheet, you create another table, p.e.
tRepWeekly, with column headers DateFrom, DateTo, WeekSum.
Into columns DateFrom, DateTo, you enter dates for first and last day of week (you can use formulas there too).
Into any of cells in column WeekSum enter the formula
=SUMIFS(tDaily[DaySum],tDaily[DayDate],">=" & [@DateFrom], tDaily[DayDate],"<=" & [@DateTo])
The column WeekSum will be filled with formula automatically.

Whenever you press Tab when last cell of table is selected, or whenever you enter something into next row below table, the table is expanded automatically. All formulas, formats, conditional formattings, and data validations, which apply for whole column of table, are expanded to new row too.

NB. When using Tables, you can't share your workbook for multi-user regime.

Edit. When you enter dates into tRepWeekly manually, and you have at least 2 rows of data in tRepWeekly, select 2 last rows for columns DateFrom and DateTo and drag down - for every row 7 days will be added to both dates.