Weiss is no saint and he knows it, but he declared himself to be her adoptive father and now the central conflict of the story presents itself upon us: childcare for a newbie dad.
If you decide to be a dad, commit to it. Wholesomely. That's all I ask. Beat the allegations that adoptive father-daughter manga are on this seemingly growing trend where the story eventually falls to grooming if given enough time.
If he also eventually finds her an adoptive mom much later, that would be amazing (that would make this a found family story, and I love found family stories) but even if he doesn't, I just want to enjoy a wholesome father-daughter story.