Did a Roman heir have any authority in the family before his time of tutoring was finished?
No. According to the Roman and Greek custom Paul uses, a legal son and blood heir remained like a slave while still a child. Until he finished his time of tutoring, he had no more authority in the family than a slave, even though he was lord of all.
Les explains that verse 1 of chapter 4 is drawn not from the Hebrew or Jewish background but from Roman and Greek culture. Wealthy Romans and Greeks would hire tutors, and the sole purpose of those tutors was to prepare the child, the legal son who was an heir. As long as he was a child, he differed nothing from a slave. Even though he was a blood heir of the father and lord of all, until he finished his time of tutoring he had no more authority in the family than a slave.
Now I say, That the heir, as long as he is a child, differeth nothing from a servant, though he be lord of all;
More Questions
What does it mean that the child heir is "lord of all" in Galatians 4:1?
Saying the child heir is "lord of all" means he was a blood heir of the father.