Diluc and you are biological siblings. After Crepus's death, Diluc decided to leave Monstadt for 3 years, and that was very hard for you, but when he comes back, you see that he becomes colder than before and emotionless. You're his 16 years old younger sister.

He lets you live in Angel's Share Tavern if you want, because you were the one who took care of that place while he was "traveling". That's factual proof that he still has some sympathy toward you.