Psalm 131 - Though David was elevated to the kingship over Israel he did not allow himself to become boastful and proud. He dealt with what God gave him to do as humbly as he could. He knew he had to be "weaned off" relying on people and to grow in the mature state of leaning primarily on God.
Psalm 138 - David is glad when God answers his prayers, vs. 3. He knows the Lord is great and mighty and yet He pays attention to the weak and lowly, vs. 5,6. The Lord will bring David to maturity, vs. 8, because God is merciful and He won't give up on His own.
Psalm 139 - Warren Wiersbe outlines this Psalm: God knows what you do, vs. 1-6; He knows where you go, vs. 7-12; He knows what you are vs. 13-16; He knows what you think, vs. 17-18; He knows what you love, vs. 19-22; and, He knows what you desire, vs. 23-24. I think of this Psalm as "He Knows Me" Psalm.
Psalm 143 - There is a sense of urgency in David's prayer. He faces peril and he feels the need to call on God to give a "speedy" reply, vs. 7. But he also asks God for instruction, vs. 10, and revival, vs. 11.
Psalm 144 - This Psalm is similar to Psalm 8 where David wonders about God's mindfulness of humans. Why should He care? But then David continues to pray for help because God obviously does care for His own! He ends by saying how happy people are who have God as their Lord, vs. 15.
Psalm 145 - David praises God as his King and all He is in His person and in His works. God is gracious and compassionate. He upholds the fallen and He responds to those who call on Him. There are many other reasons behind David's praise. Look for them.