Proverbs 16:6 Unfailing love and faithfulness make atonement for sin. By fearing the Lord, people avoid evil.
My first thought about this verse was about David... about how much He loved God.... about how David went to God with his every thought.... it made me think that David's love for God made up for the sins that David committed. Then I thought ...no it was God's great love for David that made atonement or David's sins.
What if it is the combination... David needed God's love...God's promise of sending Jesus to die for for our sins, to make atonement or our sins through such great love. And David needed to love God so much that he asked forgiveness of his sins...forgiveness for any way that he hurt God by doing wrong.
God already proved his love for us...by sending Jesus to die for our sins even before we were born. We need to prove our love for God by spending time with Him.... learning about Him, talking with Him... doing what pleases Him. Then when the world gets in the way and we mess up...God's love for us and our love for God supplies the atonement we need for our sins. Love conquers all!