What does Paul mean when he says he was comforted in the Corinthians' comfort?
Paul identified with the Corinthians, so their comfort became his comfort. Because the sin issue had been dealt with and everything was squared away, he felt what they felt: as they were comforted, he was comforted, and he rejoiced with them.
Les explains that Paul's phrase follows the Corinthians' response to the man involved in sin. Once the matter was dealt with severely and everything got squared away, Paul says, 'therefore we were comforted in your comfort.' In other words, Paul says, 'As you feel, I feel.' Their relief and joy became his. Paul also says he was exceedingly more joyed for the joy of Titus, because Titus's spirit was refreshed by the Corinthians. Titus's inward affection toward them was more abundant as he remembered their obedience and how they received him with fear and trembling.
Therefore we were comforted in your comfort: yea, and exceedingly the more joyed we for the joy of Titus, because his spirit was refreshed by you all.