one by one, beginning with the eldest
I heard Scott Hahn speaking about this incident and his thoughts were very interesting. Will try to recapture what he said:
He noted that the Scribes and Pharisees were trying to trap Jesus - discrediting Him no matter which way He answered. If He said not to stone her they could discredit Him before the people by saying He didn’t uphold the Mosaic Law; if He said to stone her they could report Him to the authorities for disobedience of the Roman law (Jews were not allowed to inflict capital punishment on their own).
Jesus, with His statement “Let him who is without sin among you be the first to throw a stone at her.” completely flips the trap they set for him, and they are the ones trapped – falling into the very trap they set for Him.
If they pick up a stone and throw it at the woman (thus claiming to any onlookers that they were without sin), they could be reported to the Roman authorities; if they walk away without stoning the woman, then to any onlookers it is like an admission that they are guilty of sin - that they have broken the Mosaic Law in some way.
**Now, finally to the verse involved in your question **-- “But when they heard it, they went away, one by one, beginning with the eldest,…”
Hahn commented on how the first ones to leave were the eldest. His thought is that they were the first (being older and wiser) to recognize the trap. But one by one, it dawned on each one and as it did, they turned and left.
PSALM 57:6 comes to mind:
“They set a net for my steps;
my soul was bowed down.
They dug a pit in my way,
but they have fallen into it themselves.”