By the time Galatians was written Peter’s ministry had diminished, along with Israel’s position (the focus of Peter’s ministry), to the point that he is not mentioned once more in the Book of Acts. It’s ALL Paul from ch. 16 to the end.
The was NOTHING for anybody in Jerusalem to add to Paul (Galatians 1, 2). Paul didn’t even offer a bone to Peter, let alone any bone fides.
I recently posted some early Church Fathers’ writings.
http://www.newadvent.org/cathen/11744a.htm#IV contains a pretty good bio of Peter.