At least on my Fire, RECENTS is now called 'FOR YOU' screen. At the top, there is a panel that toggles between the last thing you were reading/watching/etc and Weather. If you leave it on the 'last consumed' tile then you don't ever have to see the Weather tile. I don't see any way to remove Weather or change it to something else.
Personally I rarely go to the FOR YOU panel. I find it more efficient to navigate by other means. If there were an option to remove it entirely I would enable it.
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