Theophylact of Ohrid

"But that ye may know that the Son of Man hath power on earth to forgive sins - then saith He to the paralytic - Arise, take up thy bed, and go unto thine house. And he arose, and departed to his house. But when the multitudes saw it, they marvelled, and glorified God Who had given such power unto men." Jesus commanded him to carry his bed so that the event would not appear to have been imaginary, and also, so that the multitudes would see the miracle. For they thought that Jesus, Who is greater than all, was only a man.

Commentary on Matthew ↗

Gregory the Dialogist

Or by the bed is denoted the pleasure of the body. He is commanded now he is made whole to bear that on which he had lain when sick, because every man who still takes pleasure in vice is laid as sick in carnal delights; but when made whole he bears this because he now endures the wantonness of that flesh in whose desires he had before reposed.

Catena Aurea by Aquinas ↗

Hilary of Poitiers

Furthermore, so it could be understood that he was in a body and that he could forgive sins and restore health to bodies, Jesus said, "That you may know that the Son of Man has power on earth to forgive sins," then he said to the paralytic, "Arise, take up your pallet." He could have simply said "Arise," but since the reason for doing every work had to be explained, he added, "Take up your pallet and go home." First he granted remission of sins; next he showed his ability to restore health. …

Commentary on Matthew 8.7 ↗

Thomas Aquinas

Therefore, that you may know that the Son of man has power on earth to forgive sins. He shows it in deed: first, the end of the deed is mentioned; secondly, the method; thirdly, the efficacy. Hence he says, In order that you may know that the Son of man has power on earth to forgive sins, he says to the paralytic, "Rise, take up your bed and go home." By this he manifests that he is God: "He will save his people from their sins" (Mt 1:21). …

Commentary on Matthew ↗