For he longed after you all. The verb is strengthened by the preposition: "was eagerly longing." Perhaps it should be rendered. he "is longing;" like "I count it necessary," in Philippians 2:25. And was full of heaviness, because that ye had heard that he had been sick.
"Full of heaviness" ( ἀδημονῶν) is the word used of our blessed Lord in his agony (Matthew 26:37). Some derive it from ἄδημος, he away from home; others, more probably, from ἄδην, in the sense of loathing, weariness, satiety.
The word implies heart-sickness, restless; unsatisfied weariness, produced by some overwhelming distress.