DAYOFWEEK(날짜) 로 요일 체크 조건을 추가하면 될꺼같아요. 아래는 요일 확인 참고쿼리 입니다. 

WITH RECURSIVE DailyTbl AS (
	SELECT 1             AS lv UNION ALL
	SELECT 1+DailyTbl.lv AS lv FROM DailyTbl WHERE DailyTbl.lv < 15
)
SELECT 
	listdate + INTERVAL lv-1 DAY "날짜"
	, CASE 
		WHEN DAYOFWEEK( listdate + INTERVAL lv-1 DAY ) = 1 THEN '일요일'
		WHEN DAYOFWEEK( listdate + INTERVAL lv-1 DAY ) = 2 THEN '월요일'
		WHEN DAYOFWEEK( listdate + INTERVAL lv-1 DAY ) = 3 THEN '화요일'
		WHEN DAYOFWEEK( listdate + INTERVAL lv-1 DAY ) = 4 THEN '수요일'
		WHEN DAYOFWEEK( listdate + INTERVAL lv-1 DAY ) = 5 THEN '목요일'
		WHEN DAYOFWEEK( listdate + INTERVAL lv-1 DAY ) = 6 THEN '금요일'
		WHEN DAYOFWEEK( listdate + INTERVAL lv-1 DAY ) = 7 THEN '토요일'
	  END AS "요일"
	, CASE 
		WHEN DAYOFWEEK( listdate + INTERVAL lv-1 DAY ) IN (1,7) THEN 'Weekend'
		ELSE ''
	  END AS "주말여부"
FROM (
	SELECT lv , '20210401' listdate FROM DailyTbl
) DOWList;