Rashi on Psalms
A base person is despised in his eyes One who is base with his wickedness is despised in the eyes of the righteous man, e.g. Hezekiah, who dragged his father’s remains in disgrace.
Radak on Psalms
Despised is he in his own eyes, rejected: – He recounts further some of his good qualities. For although he walketh perfectly and worketh righteousness and speaketh truth, he does not pride himself upon this, but is despised in his own eyes and rejected, thinking in his heart that he cannot perform one-thousandth part of what it is his duty to do for the honour of his Creator.