All illness is rooted in sin. It started at the fall.
We are _like_ him in that we have three aspects/dimensions: body, soul and spirit. It’s not a surprise that _salvation/healing_ has three dimensions: healing, delivering and saving.
IIRC, the Greek(?) word used in the NT for “healed” and “saved” is the same word. And while illness is rooted in the Fall, I am pretty sure that Jesus was not trying to cure the man of paralysis by saying that his sins are forgiven.
I like this story as when the Pharisees were saying “Who are you to say you can forgive sins!?” So Jesus cures the guy then replies “So what is easier - to cure a man, or to SAY ‘Your sins are forgiven’”? (Or maybe he said it first, then cures the guy? Either way, sort of an “in your face” to the Pharisees!)