Their faith - Their confidence or belief that he could heal them.
Son - Literally, "child." The Hebrews used the words "son" and "child" with a great latitude of signification. They were applied to children, to grandchildren, to adopted children, to any descendants, to disciples, followers, young people, and to dependents. See the notes at Matthew 1:1. In this place it denotes affection or kindness. It was a word of consolation - an endearing appellation, applied by the Saviour to the sick man to show his "compassion," to inspire confidence, and to assure him that he would heal him.
We never saw it on this fashion - Literally, "We never saw it so." We never saw anything like this.

When Jesus saw their faith,.... The faith of the sick man, and his friends, who seemed confident, that could they get at Christ, a cure would be wrought: the faith of the one appears in suffering himself to be brought in such a manner, under so much weakness; and with so much trouble; and of the other in bringing him, and breaking through so many difficulties to get him to Christ.
He said unto the sick of the palsy, son, thy sins be forgiven thee; pointing and striking at the root of his disorder, his sins. Christ calls him son, though, in this afflicted condition a person may be a child of God, and yet greatly afflicted by him; afflictions are not arguments against, but rather for sonship: "for what son is he whom the Father chasteneth not?" He scourgeth every son whom he receiveth, and by chastising them, dealeth with them as with sons; and such as are without chastisement are bastards, and not sons, Hebrews 12:6, yea he calls him a son, though a sinful creature, and who had not, as yet, until these words were spoken by Christ, any discovery and application of pardoning grace unto him: he was a son of God by divine predestination, being predestinated to the adoption of children: he was a son by virtue of the covenant of grace, he was interested in, as appears by his enjoying pardon of sin, a blessing of it; which runs thus, "I will be their Father, and they shall be my sons and daughters", 2-Corinthians 6:18. He was one of the children which were given to Christ as in such a relation: and for the sake of whom Christ was now a partaker of flesh and blood, and in a little time was to die for them, in order to gather them together, who were scattered abroad. The blessing Christ conferred on this poor man is of the greatest consequence and importance, forgiveness of sin: it is what springs from the grace and mercy of God; it is provided in a promise in the covenant of grace; Christ was sent to shed his blood to procure it, in a way consistent with the holiness and justice of God; and this being done, it is published in the Gospel, and is a most considerable article in it, and than which, nothing can be more desirable to a sensible sinner: and blessed are they that are partakers of it, their sins will never be imputed to them; they will never be remembered more; they are blotted out of God's book of debts; they are covered out of his sight, and are removed as far as the east is from the west, even all their sins, original and actual, secret or open, of omission, or commission; See Gill on Matthew 9:2.

When Jesus saw their faith--It is remarkable that all the three narratives call it "their faith" which Jesus saw. That the patient himself had faith, we know from the proclamation of his forgiveness, which Jesus made before all; and we should have been apt to conclude that his four friends bore him to Jesus merely out of benevolent compliance with the urgent entreaties of the poor sufferer. But here we learn, not only that his bearers had the same faith with himself, but that Jesus marked it as a faith which was not to be defeated--a faith victorious over all difficulties. This was the faith for which He was ever on the watch, and which He never saw without marking, and, in those who needed anything from Him, richly rewarding.
he said unto the sick of the palsy, Son--"be of good cheer" (Matthew 9:2).
thy sins be forgiven thee--By the word "be," our translators perhaps meant "are," as in Luke (Luke 5:20). For it is not a command to his sins to depart, but an authoritative proclamation of the man's pardoned state as a believer. And yet, as the Pharisees understood our Lord to be dispensing pardon by this saying, and Jesus not only acknowledges that they were right, but founds His whole argument upon the correctness of it, we must regard the saying as a royal proclamation of the man's forgiveness by Him to whom it belonged to dispense it; nor could such a style of address be justified on any lower supposition. (See on Luke 7:41, &c.).