To be fair, while taking Weir out may have been intentional, they hadn't intended to replace Carter.
Carter should have never been commander at all. Amanda Tapping did an interview before she did Atlantis saying that she really didn't want to do the show, that she had moved on after SG-1 was canceled, but she was under contract for a season 11 that made her d her time on Atlantis.
Just another example of horrible writing. They should have never have killed Weir off, Torri Higginson was pissed when she was fired from the show. Every season of Atlantis got worse and worse and by the end it was nearly unwatchable, and at times just depressing.