again in sorrow
The translation here reads, “come to you again in sorrow” rather than “come to you in sorrow again.” The word “again” is placed before “sorrow” in order to conform more closely to the word order in Greek. Structuring the sentence the same way in English as it is in Greek (wherever grammatically acceptable) gives the reader the clearest window to the Greek text. By emphasizing “again” first, Paul communicates that he does not want to repeat the “sorrowful visit” which he apparently had with them some time prior. Rather, than having the same thing again, Paul wants his next visit to result in joy (v. 3).

abundantly
The adverb “abundantly” translates περισσοτέρως (perissoterōs). This is an intensified form of the word περισσῶς (perissōs), which communicates a very large measure or quantity of something. Thus, “abundantly” carries the intended idea better than something like “especially,” which communicates more of a quality than a quantity of something. Paul here is speaking of the exceedingly great measure of love which he has for them. His intention in writing his earlier “severe letter” was not to cause them grief but to show his love for them by helping them grow in holiness.

proven character
Many translations have something like “test you” or “put you to the test” here, and while the root idea of the word δοκιμή (dokimē) indeed carries the idea of “testing” (cf. 2 Cor 8:2), the specific grammatical construction here makes translation with that gloss difficult. The main verb in the present clause is γινώσκω (ginōskō; “know”) and δοκιμή (dokimē) is a noun functioning as the object of what is “known.” Thus, the translation here as “know your proven character” best represents the syntax of the Greek (γνῶ τὴν δοκιμὴν ὑμῶν; gnō tēn dokimēn hymōn), since something like “know your testedness” is quite awkward. This also shows consistency with the other places where δοκιμή (dokimē) is rendered as “proven character” (Rom 5:4; 2 Cor 9:13; cf. Phil 2:22). Thus, Paul says here that he chose to communicate by writing (rather than coming in person) to know their character, which would be proven by their obedience in receiving again the punished man (v. 6) after his repentance.

graciously forgive
The verb χαρίζομαι (charizomai) appears three times in this verse, and is built on the familiar Greek word for “grace” (χάρις; charis) which abounds in this letter. To help readers see this repeated emphasis on grace, χαρίζομαι (charizomai) is translated as “graciously forgive” rather than simply “forgive.” Throughout this letter, grace is the solution to sorrow or difficulty, so here, Paul encourages the Corinthian believers to restore the repentant sinner by reaffirming their love for him (v. 8), inasmuch as Paul himself has judged to graciously forgive him.

thanks
This is one of three instances in 2 Corinthians in which a word sharing the χάρις (charis) root is not translated with some form of the English word “grace” (refer to the discussion on 1:15; cf. 8:16; 9:15). This is because contextually, it is an expression of thanksgiving. Thankfulness aptly compliments grace as it is the appropriate response to receiving grace. In Greek, this is more evident because the words for “grace” and “thanks” share the same root (χάρις; charis). Because English does not have the same advantage, “thanks” is used in cases like this to give the best contextual meaning possible in English, allowing the reader to discern the inherent connection between grace and gratefulness.

leads…in triumphal procession
The Greek participle θριαμβεύοντι (thriambeuonti) is translated here as “leads…in triumphal procession.” This word was most commonly used in Roman culture to describe the action of a victory parade of a Roman general who had gloriously won a battle. Here, Paul portrays God as the ultimate victor being honored in such a procession. Regardless of painful and distressing circumstances, Paul can joyfully give thanks to God because he remembers that He is always victorious, and uses even the suffering and distress of believers to manifest the aroma of the knowledge of Him in every place, thus continually testifying of His victory.