I agree with Amane's thought process: he can't meddle in her family affairs, but at least he can be her support anchor. This is big for Mahiru, as before Amane came into her life, her future was bleak, as her parents will disown her once she is no longer a minor, but I also think they would keep an eye on her to see if she could be useful to them in the future (for money, bargaining chip, etc).
Amane entering her life has given her a potential way out of her future hell and into one with people who do care about her. I think this point is where she will become fully aware of this, which could explain her change in behavior towards Amane in volume 3 and beyond.
So far, Amane has been a fairly generic protagonist, but we haven't gotten into his backstory yet, which I believe gets explored towards the end of volume 3.