With regards to the 'why couldn't TMC Elizabeth stay' question, I assume John rationalised that because she actually didn't want to stay. Heaven knows why though. If she had wanted to, that would've been a tougher question in comparison to Gitm. This Elizabeth seemed to me to be closer to the original (I don't know why, maybe it had something to do with the fact that Torri was playing her), except for one thing. Almost from the get go she acted as if she was 'only' a copy, and never expected to have her former life back. But she did hold true to Elizabeths other beliefs, and was in fact instrumental to ending the war with the replicators. Perhaps she was more like the real Elizabeth than she realised?
As to why they didn't accept TMC Weir vs accepting Kindred Carson, I think it has a lot to do with attitude. Carson II thought he was the real thing. It was only when he got back to Atlantis that he found out he wasn't. Since his cloning he had acted as the other Carson would, and continued to do so after his return (well, no more OOC than any of the other leads in s4/5).
With Gitm
As to why they didn't accept TMC Weir vs accepting Kindred Carson, I think it has a lot to do with attitude. Carson II thought he was the real thing. It was only when he got back to Atlantis that he found out he wasn't. Since his cloning he had acted as the other Carson would, and continued to do so after his return (well, no more OOC than any of the other leads in s4/5).
With Gitm
Spoiler:
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