Now, these commentators call it a psalm of sickness; they say it contains no confession of sin. But when you look at it as the sickness being a metaphor for sin, as illness was generally considered a result of sin, so asking for healing, which he does in verse 2, can be seen as a parallel to seeking God's forgiveness.
Now if we look at this with a literary view in mind, we can see that David is hinting that it is not really his sickness that he is talking about. It is something was the matter with his soul, something was the matter inside, something was the matter with his whole being. And I mean, the psalm opens with David pleading for God's mercy because he believes he is suffering under God's wrath. "Do not rebuke me in Your anger," in Your wrath, "nor chasten me [discipline me] in Your hot displeasure."
He is saying, "God, have You noticed? You're mad at me. Why are You mad at me? Why am I suffering like this? I know that something is wrong. My body feels it. I need Your mercy. Please heal me, because obviously You're not pleased with me at all. Otherwise You wouldn't have done this to me. If You were pleased with me, You'd bless me, right?" One would think so.
So obviously, at the least, David is conscience-stricken. He has a sense of sin, that there is some sin that he has not repented of, and it is causing this great chasm, this rift between God and himself. There is some weakness that he has not overcome. He uses that word in verse 2: "for I am weak." He could mean that he was physically weak, or he could mean that he was spiritually weak.
He prayed to God for mercy, you see that obviously in verse 2. But then he says at the end of verse 3, "how long?" How long are You going to leave me like this? Because God obviously had not forgiven him yet. God had not shown mercy yet. "My soul is also greatly troubled; but You, O Lord. . ." He kind of cannot finish the sentence, like maybe he was going to say, "You haven't done anything. You're still far off. Why haven't You responded to me?" And so we get "how long?" How long is it going to be that I am going to have to suffer like this before You are done chastening me in Your wrath?