You need to use the DAYOFWEEK function

If the End of the Week in Saturday, any date can be morphed into a Saturday.

For example, this computes the upcoming Saturday

    SELECT DATE(NOW() + INTERVAL (7 - DAYOFWEEK(NOW())) DAY);

For a table called mytable with a Date Column called theDate, your summation would be

    SELECT COUNT(1) DateCount,EndOfWeekDate FROM
    (
        SELECT DATE(theDate + INTERVAL (7 - DAYOFWEEK(theDate)) DAY) EndOfWeekDate
        FROM mytable
    ) A GROUP BY EndOfWeekDate;

If you have a different day of the week as the end of week, let me know and I will rewrite the query.

Give it a Try !!!