@RandomGuy It's usually the bride's family that pays the dowry. Since Petra is going to rule Brigid, she takes the "groom's" position. Also, I headcanon Dorothea being adopted into House von Hresvelg, because of all she's done for the Empire, and Edelgard just loves her. I can just imagine El going full mom-zilla on the wedding plans.
Since she's going to marry Petra anyway, might as well get a few treaties out of the deal.