Matthew Poole and continuators on 1 Samuel 24:16

16 ¶ And it came to pass when David had made an end of speaking these words unto Saul, that Saul said, Is this thy voice, my son David ? And Saul lift up his voice, and wept .

He knew his voice, though being at a great distance from him, he could not discern his face.

Partly, from the sense of his sin against God, and of his wicked and base carriage to David, (for there are some such Temporary passions oft-times in Hypocrites and ungodly men) and principally from the remembrance of so great and so late a danger as he had now escaped; which commonly produceth grief and tears; as 2 Sam. 13. 36. Yet these may be tears of affection or tenderness (upon the sense of David's kindness) rather than of grief.