In which we discuss TVTropes pages which are either full of shit or clearly ill-thought. Obviously, if this thread gets any traction at all, there will be many links to the wiki in question. Sorry about that.
Clearly both can’t be true, and the true weather trope for funerals is that the weather at a cinematic or television is a complete tossup, based on the actual weather on the day of shooting, access to a rain-simulation machine, and the whims of the director(s) and screenwiter(s).
If you want to do a thread talking about TV Tropes, why not just start a thread titled “Let’s Talk About TV Tropes?”
But your OP as stated makes no sense at all. TV goes toward extremes for dramatic purposes. So it can go to both ends of the extreme at different times. Both can be clichés and both can be overdone. Big deal.
If I were you I’d ask a mod to close this and start over.
For starters, the two examples the OP mentions should probably be lumped together under Pathetic Fallacy (which TVTropes probably already has a page for, but I’m not going to be the one to check). Which also has the advantage that it’s a trope that was recognized as such long before the Internet.