All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
We have already issued Fataawa 88368 and 87169 clarifying the categories of people who are eligible for Zakah. Therefore, if your aunt is amongst those categories and she is in need of her son to spend on her, then it becomes permissible for you to pay the Zakah on your money to her. Rather, paying the Zakah to her is better than paying it to a stranger because you get double reward in giving Zakah to a relative; the reward of Zakah and the reward of keeping ties with him/her.
It is also permissible to pay your Zakah to your cousin if he is completely or partly unable to meet the expenses of his wedding. However, if he is only partly unable to meet the expenses of his wedding, then you should only give him what will be enough for him to meet his needs without any extravagance.
Allaah Knows best.