Literally, the end of this verse reads, His soul was shortened unto death.
Delilah had worn down Samson to the point where he could no longer withstand her. Notably, this is the second time in the book that we come across the expression, His soul was shortened.
In Judges 10:16, it was used with reference to the Lord, whose soul became short with the misery of Israel.
That is, he became weary of, exasperated with Israel's suffering. He saw Israel’s situation as intolerable: he was offended by his people’s efforts to manipulate him into doing what they wanted, and he was weary of their continued misery, weary of their conversions of convenience. Now in Judges 16:16, it is said that Samson’s soul was wearied to the point of death.
He became weary of her badgering him for his secret. The situation became intolerable for him.
16 And when she pressed him hard with her words day after day, and urged him, his soul was vexed to death.