Brother and sister are the gendered names for children having the same parents.
"bro", in this case is short for "brother".
That said, I don't know where African Americans got it from, but labor unions used the terms brother and sister going back to their beginnings in the 1800s. So it may have been copied from that.
Anyway, I think it migrated from surfer culture to fratboy culture. There, it acquired a tinge of elitism and sexism, because... well, frats are elitist and sexist.