I don't know where they got those numbers from, but the best thing to do is go straight to the horse's mouth...
https://www.usa.canon.com/shop/p/eos-r5-mark-ii
R5 + battery + CFe card: 738g
R5ii + battery + CFe card: 670g
My guess is that R6 III will spill into the 700g and above weight class...
It's possible that a CFe card (if they add it) plus a multi-angle tilting LCD display (if it gets one) could add a bit of weight. However I wouldn't put it past the Canon engineers to actually reduce the weight of the R6ii (now 680g with battery + SD card) like they did with the R5ii.
Nikon are making their bodies heavier.
Which is part of their cachet and appeal.
OTOH one of my Nikon-toting shooting buddies has just purchased an entire OM System kit (OM-1 Mark II + lenses) to help ease that massive load!
The Z6 III is at 760g is heavier than R5 II.
And an even more apples-to-apples comparison would actually be the chunky ol' Z8 @ a hefty 910g!
Whenever I shoot with a Z8 combo (or the granddaddy Z9) I am so thankful to be shooting Canon. And for many reasons beyond weight alone!