I am going to answer this using recent SQL Server syntax. You will need to figure out how for older SQL Server and for MySQL. Some of the principals are the same.
UPDATE datetable
set wkstartdate = DATEADD(day, - DATEPART(day, cast(cast(date as varchar(8)) as date)) % 7,cast(cast(date as varchar(8)) as date))
, Week = 'W' + CAST(DATEPART(day, cast(cast(date as varchar(8)) as date)) / 7 as varchar(1))
, day = DATEPART(day, cast(cast(date as varchar(8)) as date))