Si almacena the_date como entero, primero debe convertirlo a fecha y hora usando FROM_UNIXTIME función:
SELECT SUM(`amount_sale`) as total
FROM `sales`
WHERE `payment_type` = 'Account'
GROUP BY WEEK(FROM_UNIXTIME(`the_date`))
ACTUALIZAR :
Además, es posible que desee generar el número de semana,
SELECT CONCAT('Week ', WEEK(FROM_UNIXTIME(`the_date`))) as week_number,
SUM(`amount_sale`) as total
FROM `sales`
WHERE `payment_type` = 'Account'
GROUP BY WEEK(FROM_UNIXTIME(`the_date`))
