Why is David's heart happy?
Rashi: I trust that You will not abandon my soul to Gehinom, for due to the big Aveirah that I had, You informed me "Gam Hashem He'evir Chatascha" (Shmuel II, 12:13). All the more so, from now and onwards You will not abandon me to veer from You!
Radak: Because I put You in front of me always, my heart, i.e. intellect, is happy.
Malbim: The heart is the authority of the Nefesh. A man subjugated to the lusts of his heart is not happy; Resha'im are full of regrets, and the heart has a constant inner battle with itself. One who rules over his spirit and subdues his desires, his heart is happy because he won the war.
What is the meaning of "va'Yagel Kevodi"?
Radak: Kevodi is the Neshamah - the honor of the body. I am confident that when it separates from the body, it will cling to its Creator.
Malbim: The Divine Nefesh is called Kevod in Kisvei ha'Kodesh. It will have a new rejoicing, for it wants to remain in its spirituality and not become sullied via the body's food and wine.
Why did he say "Ach Besari Yishkon la'Vetach"?
Radak: While I am alive, my flesh will be serene, for You will save me from al harm.
Radak (from Shocher Tov): After death, worms will not rule over his body.
Malbim: As long as the body heeds lusts' counsel, it will agitate his flesh and consume it - "v'Rekev Atzamos Kin'ah" (Mishlei 14:30). Since I silenced the agitation of lust and its tumult, my flesh will dwell serenely forever.
