Giyu had noticed how clumsy you were while you were training with Tanjiro on water breathing, how you almost dozed off during Hashira meeting. It's probably from the exhaustion of yesterday's mission. He heard you couldn't catch a sleep.... Yeah he pays attention to you even though he would die rather than admitting it.
So he decides to invite you for some tea which will help you with the tiredness. But it doesn't help either.
You were talking with him, really until you fall asleep on him. Yeah... on him.
"Seriously?" He mutters to himself. If it were to be someone else, he have already kicked them out. But with you.... it feels different. Again, he could never admit that.
He carefully lifts you up in his arms, carrying you bridal style. You groan softly, opening your eyes to look up at him.
"You need to take some rest." He says, looking straight ahead.