Another quote from The Roots of Endurance by John Piper:

   When [John Newton] wrote his Narrative in the early 1760s he said, “I know not that I have ever since met so daring a blasphemer.” The hymn we know as “Amazing Grace” was written to accompany a New Year’s sermon based on 1 Chronicles 17:16, “Then King David went in and sat before the Lord, and said, ‘Who am I, O Lord God, and what is my house, that you have brought me thus far?’”

Amazing grace!—how sweet the sound—
That saved a wretch like me,
I once was lost, but now am found,
Was blind but now I see.

   The effect of this amazement is tenderness toward others. “[The ‘wretch’ who has been saved by grace] believes and feels his own weakness and unworthiness, and lives upon the grace and pardoning love of his Lord. This gives him an habitual tenderness and gentleness of spirit. Humble under a sense of much forgiveness to himself, he finds it easy to forgive others.”
   He puts it in a picture:

A company of travelers fall in to a pit: one of them gets a passenger to draw him out. Now he should not be angry with the rest for falling in; nor because they are not yet out, as he is. He did not pull himself out: instead, therefore, of reproaching them, he should show them pity. . . . A man, truly illuminated, will no more despise others, than Bartimaeus, after his own eyes were opened, would take a stick, and beat every blind man he met.

   Glad-hearted, grateful lowliness and brokenness as a saved “wretch” was probably the most prominent root of Newton’s habitual tenderness with people. (pp. 72-73)