What do we learn from "ha'Sole'ach l'Chol Avonaichi"?
Nedarim 41a: A sick person is not cured until all his sins are pardoned.
Yerushalmi Brachos (2:3): This teaches that illness cleanses [the body]. Therefore, R. Yanai would wear [Tefilin the entire day] after being sick, for three days (ha'Gaon Rav C. Kanievsky, Ztz"l).
Radak: This is one of the greatest benefits that Hashem does for you. The Yud at the end of Avonaichi is extra, to beautify the expression, like "b'Socheichi Yerushalayim" (Tehilim 116:19).
Malbim: This is "Kol Gemulav" (verse 2).
What is the meaning of "ha'Rofei l'Chol Tachalu'aichi"?
Radak #1: This refers to illnesses of the Nefesh, i.e. sins 1 . The first part of the verse is repeated in different words. This is like "Refa'ah Nafshi Ki Chatasi Lach" (41:5).
Radak #2: This refers to bodily illnesses. The Nefesh is afflicted via affliction of the body, even though bodily illness does not strike the Nefesh. "Ha'Sole'ach] l'Chol" means the majority 2 ; Hashem does Chesed with a person, and punishes only for a minority of his sins - "Nosei Avon v'Over Al Pesha" (Michah 7:18).
Lev Eliyahu (Shemos p.194): It refers both to bodily illnesses and illness of the Nefesh.