Changing multiplier based on cell value

You'll need real dates for this.

So, to generate your dates, for example:

=LET(d,DATE(2025,1,1),SEQUENCE(DAY(EOMONTH(d,0)),,d))

and to allocate points:

=IF(F2:F32="","",LOOKUP(WEEKDAY(E2#,2),{1,6,7},{"",4,6}))

See in the attached workbook.

When they has attended more than seven Saturdays and/or Sundays, they receive 5 points for Saturdays and 7 points for Sundays.

This is more complcated when you have all of your months on separate tabs. Is it REALLY necessary to have one tab per month? I have not yet worked this requirement into the formula.