Father child bonds do not just break up when a child finds out a man is not her father. While it may seem odd to some people the reality is a parental bond is not necessarily formed by blood or even by marriage. It sounds like he has been a father figure to her for a long time and that is something that does not change simply because they are not related to each other. As for his age and looks, a child does not care about those things like other people would. In her mind he is the closest thing to a father figure and she wants to spend time with him regardless of wither they are truly related or not.
Since they only spend time together once a week, its perfectly normal at her age to spend time with him. Now if it was more often then yes most girls her age would shy away but if this time has been reserved for all these years then it is more a routine then anything and since they do have a father/child relationship with each other its unlikely that the young girl would see a problem with this at her age.
A bond that has continued for this long isn't going to just stop because she is a teenager, and nor should it. If he has been there for her all these years he should continue to be there as often as the child lets him be. As she grows older she may distance herself more, as is normal with children but that bond is not likely to ever disappear and there will always be a relationship. This is normal, and blood or marriage is not what makes a family work. While it may seem odd to someone who has never been in such a position but children can and do form bonds with adults that were once a part of their lives, and a good man stands firm on this bond and nurtures it regardless. If he just walked away from this child then I would question his integrity as a man.