VINE'S EXPOSITORY DICTIONARY
"Adoption" is a term involving the dignity of the relationship of believers as sons; it is not a putting into the family by spiritual birth, but a putting into the position of sons.
Please note how Paul shows the "position of sons" being that of "heirs of God" in the context of Rom 8:15: 16 The Spirit itself beareth witness with our spirit, that we are the children of God: 17 And if children, then heirs; heirs of God, and joint-heirs with Christ; if so be that we suffer with him, that we may be also glorified together.
Among Hebrews, only the firstborn son was the legal heir. But here God makes each and every believer a legal heir.
'Among the early Hebrews, as well as among many other nations of antiquity, custom decided that the next of kin should enter upon the possession of the estate of a deceased person. The first-born son usually assumed the headship of the family, and succeeded to the control of the family property... Jewish Encyclopedia.