Wept sore - Wept much. Greek: “There was a great weeping of all.”
And fell on Paul’s neck - Embraced him, as a token of tender affection. The same thing Joseph did when he met his aged father Jacob, Genesis 46:29.
And kissed him - This was the common token of affection. See the Matthew 26:48 note; Luke 15:20 note; Romans 16:16 note; 1 Corinthians 16:20 note.