Read my other posts. David's sins were not excused but were remitted as also in the case of Abraham who formerly was an idol worshipper. They believed God and their "faith was reckoned as righteousness." Read the book of Romans 4:1-8. This is the wonder of God's grace. God did not overlook their sins but as Romans 4:7,8 says, "Blessed are those whose lawless deeds have been forgiven, and whose sins have been covered. Blessed is the man whose sin the Lord will not take into account".