7:7a and not only by his arrival,

but not only by means of his coming,
-or-
In addition to that,

7:7b but also by the comfort he had received from you.

but ⌊we (excl.) were encouraged⌋ by the news of you (plur.) encouraging him.
-or-

⌊God comforted us⌋ when we heard that you comforted him.

7:7c He told us about your longing,

For he reported to us that you really wanted to see me,
-or-
He told us that you desired very much to see me,

7:7d your mourning, and your zeal for me,

that you sorrowed much, and that you were eager ⌊to do anything⌋ for me,
-or-
that you were very sad/sorry, and that you are strongly committed to me.

7:7e so that I rejoiced all the more.

so now I rejoiced even more.
-or-
So ⌊all those things made⌋ my joy even greater ⌊than before⌋.

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