The following will work for the any interval in this decade (522 weeks, from 01-JAN-2000 until 31-DEC-2009).

Code:
SQL> select * from my_table;

        ID START_DAT END_DATE
---------- --------- ---------
         1 16-JUN-02 30-JUN-02
         2 04-AUG-02 25-AUG-02

SQL> SELECT a.id, b.start_date, b.end_date
  2  FROM my_table a, 
  3    (SELECT (ROWNUM-1)*7+NEXT_DAY('01-JAN-2000','SUNDAY') start_date,
  4         ROWNUM*7+NEXT_DAY('01-JAN-2000','SUNDAY') end_date
  5     FROM all_objects
  6     WHERE ROWNUM <= 522) b
  7  WHERE b.start_date >= a.start_date
  8    AND b.start_date < a.end_date; 

        ID START_DAT END_DATE
---------- --------- ---------
         1 16-JUN-02 23-JUN-02
         1 23-JUN-02 30-JUN-02
         2 04-AUG-02 11-AUG-02
         2 11-AUG-02 18-AUG-02
         2 18-AUG-02 25-AUG-02

SQL>