Listening To Backbiting (Gheebat)
Yes, it is a sinful activity. By continuously becoming a part of this activity, instance after instance, one does become a guilty party as well. See it as a good opportunity to fulfil religious duty of ‘ amr bil maruf wani anil munkir ‘ which is required of every Muslim. However, this should be done with wisdom and not haphazardly i.e. you should instead of rebuking your cousin directly, point him to the fact that what good is this talking behind someone’s back going to do to him? other than the fact that you are both becoming a party to the sin and in fact doing the other person a favour for the day of judgement by losing your good deeds to him. And even after adopting this strategy a few times, he does not stop; then you can be straightforward about it and deny to become a part of this talk which involves backbiting.