Jamieson, Fausset and Brown on 2 Corinthians 1:14

14. in part--In contrast to "even to the end": the testimony of his life was not yet completed [Theophylact and Bengel]. Rather, "in part," that is, some of you, not all [Grotius, Alford]. So in 2Co 2:5; Ro 11:25. The majority at Corinth had shown a willing compliance with Paul's directions in the first Epistle: but some were still refractory. Hence arises the difference of tone in different parts of this Epistle. See Introduction.

your rejoicing--your subject of glorying or boast. "Are" (not merely shall be) implies the present recognition of one another as a subject of mutual glorying: that glorying being about to be realized in its fulness "in the day (of the coming) of the Lord Jesus."