2つの日付の間の週

ウィンドウ関数はあなたの友達です：

SELECT week_num,
       min(d) AS start_date,
       max(d) AS end_date
FROM (SELECT d,
             count(*) FILTER (WHERE new_week) OVER (ORDER BY d) AS week_num
      FROM (SELECT DATE '2018-09-05' + i AS d,
                   extract(dow FROM DATE '2018-09-05'
                                    + lag(i) OVER (ORDER BY i)
                          ) = 1 AS new_week
            FROM generate_series(0, DATE '2018-09-27' - DATE '2018-09-05') AS i
           ) AS week_days
     ) AS weeks
GROUP BY week_num
ORDER BY week_num;

 week_num | start_date |  end_date  
----------+------------+------------
        0 | 2018-09-05 | 2018-09-09
        1 | 2018-09-10 | 2018-09-16
        2 | 2018-09-17 | 2018-09-23
        3 | 2018-09-24 | 2018-09-27
(4 rows)