What is the meaning of "Amarti"?
Rashi: I thought.
What do we learn from "Olam Chesed Yibaneh"?
Sanhedrin 58b: Normally, one may not marry a sister. Kayin was permitted, in order to populate the world. (Rashi 58b - this is why regarding the Isur to marry one's sister, it says "Chesed Hu" (Vayikra 20:17) - it was permitted to Kayin amidst Chesed.)
Rashi #1: The throne of David will be built forever built with Chesed - "v'Chonanti Es Kisei Mamlachto" (Shmuel II, 7:13).
Rashi #2: The world will be built on Your Chesed, and You will establish Your Emunah in Shamayim, so it will be established and lasting. This refers to what You promised to David via Nasan ha'Navi - "Karati Bris li'Vchiri" (verse 4), to establish his seed forever.
Radak: The Chesed that You did to David, to give kingship to him and his sons after him [will be forever].
Malbim: The two Midos (Chesed and Emes) were revealed together at the creation. The creation was initially via pure Chesed. There was not yet existence to which Hashem could promise continuity.
What does the verse teach about Shamayim?
Radak: Just like Your Emunah is in Shamayim - You prepared that it will not cease - "ki'Ymei ha'Shamayim Al ha'Aretz" (Devarim 11:21) - so Your Chesed to David [will not cease].
Malbim: After Hashem created the world via Chesed, and established natural laws, His Midah of Emunah was established, they he will perpetuate them. This is from Shamayim, i.e. the world of spheres and below.
