I would like to calculate, in code, and without iterating through the sheet
Ya got me!

Why is that so critical?

I bet one of our Formula experts could write a cell formula that could do it. I can do that, as long as I use a helper column with a WeekDay function.

Helper Column (C) Formula ---- "=IF(WEEKDAY(A1,2)=1,1,0)"
Count of mondays formula -----"=SUM(C1:C16)"
Sum of Monday Values Formula "=SUMIF(C1:C16,1,B1:B16)"