Okay, this doesn't seem too difficult.

Your A1 date is "any start date" and your B1 date is "any subsequent
Friday", correct? And you want to know how many full weeks and partial
weeks (counted as full) occur between A1 and B1.

Then the formula in C1 should be:
=CEILING( DATEDIF( A1, B1, "d") / 7, 1)

This will:
Determine the days between A1 and B1 (DATEDIF),
Divide that by 7 (to get "weeks" and "partial weeks" as a decimal),
Round that upward (if necessary) to the nearest whole number (CEILING).

Chris