George Dorset is the quintessential House of Mirth husband. He makes a lot of money, he doesn't say much, and his wife has him completely under her thumb. As Mrs. Trenor says, "The poor creature can't stand alone. And I remember him such a good fellow, full of life and enthusiasm" (2.5.29).
Bertha has sucked George Dorset dry. He's so completely under her power that, even when he knows she's having an affair with Ned Silverton, he can't bring himself to do anything about it. We never see the scene where Bertha convinces him to stay with her, but we do see its aftermath, through Selden's eyes:
Though Dorset's attitude had perceptibly changed, the change was not clearly to be accounted for. It had certainly not been produced by Selden's arguments, or by the action of his own soberer reason. Five minutes' talk sufficed to show that some alien influence had been at work, and that it had not so much subdued his resentment as weakened his will, so that he moved under it in a state of apathy, like a dangerous lunatic who has been drugged. (2.3.10)
That's most certainly Bertha's work.
Meanwhile, George reminds us that it's not only women who are confined by the gilded cage of society, or suffering at the fate of social determinism. It's George's role to be quiet and make money, as much as it is Lily's role to be charming and beautiful. And, while Lily finds herself chained down, so, too, does George. "I'm desperate – I'm at the end of my tether," he tells her. "I want to be free, and you can free me. I know you can. You don't want to keep me bound fast in hell, do you?" (2.6.25)
George is as much the victim of his environment as Lily, as both are sacrificed at to keep the social machine running smoothly. Does all of society believe Bertha's story about George and Lily, and her innocence regarding Ned Silverton? Of course not, but as Lily pointed out, it's easier to believe Bertha. Society collectively decides to sacrifice people like Lily or George; it makes for fewer bumps in the road.