4 But when the set time had fully come, God sent his Son, born of a woman, born under the law, 5 to redeem those under the law, that we might receive adoption to sonship. 6 Because you are his sons, God sent the Spirit of his Son into our hearts, the Spirit who calls out, “Abba, Father.” 7 So you are no longer a slave, but God’s child; and since you are his child, God has made you also an heir.
It's a bit trite at times to trot out the idea that Abba in Aramaic was closer to Daddy than Father in tone. There's a sense of intimacy there that you don't get with "father", which you have to have a good English schoolboy accent to pull off with a straight face when addressing your dad.
When you go back to all those classic hymns, they are using the intimate second person rather than the formal third person; instead of being stuffy and archaic, the thees and thous are actually the abba-daddy format that were used for freinds and loved ones. We'd have to redo our modern love songs if we kept that, where I would have grown up with Thou Makest Me Feel Brand New or Thou Lightest Up My Life.
We're heirs of God. However, we'll never actually inherit much, since God doesn't die, (unless Neitzsche gets in on things) but we share in God's kingdom as His sons and daughters. Not bad.