I encountered the phrase in this line:
あいつはあいつで、きちんとバイトしているらしい。
I think I can intuit the general meaning but I was wondering if anyone had a full explanation.
「あいつはあいつで~~」 means "He ~~ in his own way."
As the word 「きちんと = "properly"」 may suggest,
"Pronoun X + は + Same Pronoun X + で"
expresses the speaker's opinion that the Person X is doing something at least on a satisfactory level if not on an extraordinary level.
「これはこれでおいしい。」 = "This dish tastes OK if not spectacular." ==> "It tastes good in its own way."
One can also use a real personal name instead of a pronoun in this expression as in.
「スミスはスミスでちゃんと働{はたら}いている。」