Why did Paul send Timothy to the Philippians?
Paul sent Timothy so that the Philippians, upon seeing him again, might rejoice, and so that Paul himself might be less sorrowful. This was set against their constant persecution and circumstances, yet they could still have joy. He wanted their reunion to produce joy in them and ease his own sorrow.
Les explains from Philippians 2:28 that Paul sent Timothy "the more carefully" so that when the Philippians saw him again they might rejoice, and so Paul would be less sorrowful. Les connects this to the believers' situation: they were under constant persecution, yet they could still be full of joy. He distinguishes joy from happiness, noting that even if one's little world falls apart, believers are still supposed to be joyful. The theme continues into Philippians 3:1, "finally my brethren, rejoice," and Philippians 3:3, where they rejoice in Christ Jesus and have no confidence in the flesh. Timothy's sending therefore related to their joy and Paul's relief.
I sent him therefore the more carefully, that, when ye see him again, ye may rejoice, and that I may be the less sorrowful.