John Gill Commentary Psalms 51:9

"Hide thy face from my sins, And blot out all mine iniquities." — Psalms 51:9 (ASV)

Hide your face from my sins
In whose sight they were committed, being now ashamed of them himself, and ashamed that any should see them, and especially his God; and being filthy and nauseous, he knew they must be abominable to him, who is of purer eyes than to behold iniquity; and being breaches of his law, must be offensive to him, and provoke the eyes of his glory; and were such that he knew would not bear the examination of justice; and that if God was strict to mark them, he could not stand before him.

Moreover, in this petition the psalmist deprecates a severe chastisement of them, which is sometimes expressed by setting sins before him, (Psalms 90:8) ; and entreats the pardon of them, or oblivion and non-remembrance of them, that they might be cast behind his back, and into the depths of the sea;

and blot out all my iniquities ;
as in (Psalms 51:1) ; here repeated, to show his deep sense of them, and his great importunity for the forgiveness of them; and adds the word all, including all his other sins, with those he had lately committed; for he knew that, if anyone, was left unpardoned, he could never answer for it.