Probably easier to have records expiring than the database.
Include a timestamp field to record when the records are added
Each week on Friday
select * from mytable where timefield between '$mondate' and '$fridate'
write these records to a csv file or tab delim file
Optionally (though not necessary) when you are sure you have the data :-
delete from mytable where timefield between '$mondate' and '$fridate'
hth