Albert Barnes Commentary Psalms 41:11

"By this I know that thou delightest in me, Because mine enemy doth not triumph over me." — Psalms 41:11 (ASV)

By this I know - Compare the notes at (Psalms 20:6). This indicates a confident assurance that his prayer would be answered, and that he would be restored to health. How he had this assurance we are not informed, but it seems most probable that it was by an intimation conveyed to his mind by God himself. Compare, for a similar case, (Philippians 1:25). See the notes at that passage.

That you favor me - That you do delight in me; that you are my friend.

Because my enemy does not triumph over me - The word here rendered triumph properly means to shout, or to make a noise, as a sign of exultation, more especially in war (1 Samuel 17:20). Here it means that his enemy would not secure a victory over him, or would not shout as if such a victory were obtained. That is, he felt assured now that all the machinations of his foes would be defeated; that all the hopes which they cherished that he was soon to die would be disappointed; that he himself would be recovered from his sickness, contrary to their malicious anticipations and desires. This he regarded as an evidence that God was his friend.