Your version is [very antiquated and insecure. For reference 8.2 was last supported in 2011. It was released in 2006.](https://www.postgresql.org/support/versioning/) It lacks

* tstz ranges
* window functions 
* lateral joins

Moreover, we can't easily configure your setup to test our queries. Upgrade your version PostgreSQL; if you find that difficult to do, consider seeking out a consultant.

I think what you want is something like

    SELECT member_id, t2.date, count(*)
    FROM t AS t1
    CROSS JOIN t AS t2
      ON ( member_id )
    WHERE t1.date_date BETWEEN t2.date AND t2.date_date + '7 days
    GROUP BY member_id, t2.date
    HAVING count(*) >= 7;

But I can't test it and you didn't provide `CREATE TABLE` or `INSERT` statements.