Bogus. At best, "... yet."
Entire sports teams of children board planes filled with adults, without redistribution. They need to weigh every passenger now, just in case they might need to move that 1 larger person? If you buy that then I've got some oil you'd be interested in.
As far as I can tell, 1 commercial plane in history has had an accident due to balance and only because of tragically bad maintenance at the same time.
This looks like one of the more obvious cases of groundwork being laid for future fees veiled in safety concerns.
The bottom line for me personally is that it's just one more bullshit thing to endure when traveling via plane, and I'm biased against them at this point. Airlines are the skeeziest companies in their attempts to capture market surplus.
The Norwegian regional carrier Widerøe (Whose slogan might well have been "We proudly fly where everyone else is scared s--tless to!", operating a fleet of small to mid-size aircraft always play a game of musical chairs in their smaller (<40pax or so) planes prior to takeoff.
Edit: Ninja'd by gragas.
It ONLY is about properly distributing weight. It's not a fat tax. It's not "oh, this person is heavy compared to their height, let's charge them more because they're inferior!".
It's only "we need more weight in the front".