Please don't apologize. I'm also busy on weekdays, so I often can't respond until the weekend or the holidays.
ご質問ありがとうございます。
"Please don't apologize."=「謝らないで下さい。」
"I'm also busy on weekdays,"=「私も平日は忙しいです」
"so I often can't respond until the weekend or the holidays."=「なので私も多くの場合、土日か祝日ではないと返信が出来ません。」
☆または、"so I often end up replying on Saturdays, Sundays, or on holidays."=「なので土日、あるいは祝日に返信してしまうことが多いので」という表現も使えます。