You can use the general calc shown below to get the nearest day of any day:

SELECT

date,

DATEADD(DAY, DATEDIFF(DAY, '19000101', date) / 7 * 7, '19000101') AS monday_on_or_before_date,

DATEADD(DAY, DATEDIFF(DAY, '19000102', date) / 7 * 7, '19000102') AS tuesday_on_or_before_date,

DATEADD(DAY, DATEDIFF(DAY, '19000103', date) / 7 * 7, '19000103') AS wednesday_on_or_before_date

FROM (

SELECT GETDATE()-3 AS date UNION ALL

SELECT GETDATE()-2 AS date UNION ALL

SELECT GETDATE()-1 AS date UNION ALL

SELECT GETDATE() AS date UNION ALL

SELECT GETDATE()+1 AS date UNION ALL

SELECT GETDATE()+5 AS date UNION ALL

SELECT GETDATE()+11 AS date

) AS test_dates

Once that calc gets you the first date you need, you simply add -7, -14, -21, etc., days to go back as many weeks as you want.

For example, for the last 6 Mondays on or before the current date (whatever that is when the code is run):

SELECT

DATEADD(DAY, days_to_add, most_recent_monday) AS last_6_mondays

FROM (

SELECT DATEADD(DAY, DATEDIFF(DAY, '19000101', GETDATE()) / 7 * 7, '19000101') AS most_recent_monday

) AS main_date

CROSS JOIN (

SELECT 0 AS days_to_add UNION ALL

SELECT -7 AS days_to_add UNION ALL

SELECT -14 UNION ALL

SELECT -21 UNION ALL

SELECT -28 UNION ALL

SELECT -35

) AS days_to_add

ORDER BY 1