Here are some of the most common lenses...
24-70 f/2.8 Sony 886 g, Canon 900 g
24-105 f/4 Sony 663 g, Canon 700 g
70-200 f/4 Sony 840 g, Canon 695 g
24-240 f/3.5-6.3 Sony 780 g, Canon f/4-6.3 751 g
100-400 f/4.5-5.6 Sony 1395 g, Canon 100-500 f/4.5-7.1 1365 g
As you can see, the weights are almost all very close. Prices very close, too. Why the constant forum opinions that Sony is somehow lighter, smaller and cheaper? They are not.
If you are looking for smaller and lighter, some of Nikon's Z standard zooms are indeed smaller and lighter. enough of a difference that I briefly switched from Canon to Nikon last year. But Canon color brought me back. That, plus the new RF 100-400 - a lens that truly is much lighter than any 100-400 lens we have ever seen.
Why are there opinions that Sony is lighter, smaller and cheaper? Well, so far as the Sony
system goes, here is my start on an explanation ...
Sigma 85 f/1.4 DN for Sony is 625g and A$1,700, while the Canon RF 85L is 1195g and about A$3,750 (on sale - a lot of places have it at almost A$4,300!).
Samyang 75 f/1.8 for Sony is 230g and A$500. Sony 85mm f/1.8 371g andA$700. Canon RF 85mm f/2 497g and A$950. In my opinion, the Sony has better optics than the Canon (and probably faster AF too). I think the same can probably be said for the Samyang - and even if it is no better optically than the Canon, it is certainly lighter and cheaper.
Sony 55 f/1.8 is 280g and A$850 while Canon really doesn't have anything I'd call comparable. The Sony may not be up to the standard of the RF 50L but in my opinion it is far better than the Canon RF 50 f/1.8.
Samyang 45 f/1.8 for Sony is 162g and A$500. Canon RF 50mm f/1.8 is 160g and and A$300. The Samyang is more expensive in this case, by in my opinion it is better optically and worth the extra money.
Sigma 24-70 f/2.8 DN for Sony is 835g but A$1,600 while the Canon RF L is 900g but about A$3,350.
Tamron 70-180 f/2.8 for Sony is 810g and A$1,650 while the Canon RF 70-200 f/2.8L IS is 1070g and A3,900. (OK, all else being equal, I would prefer the Canon in this case, but not at the price difference.)
Sony 50 f/1.2 GM is 778g and A$3,000. Canon RF 50 f/1.2L is 950g and A$3,500. (OK, there is not very much difference in that one.)
Sony 35 f/1.4 GM is 525g and A$2,100 while the Canon RF is ... well, we shall have to wait and see. However, the Canon EF 35 f/1.4L II is 760g and A$2,700, and so far most RF lenses have ended up being heavier and more expensive than their EF counterparts (although to be fair, some have been lighter).
I'm a long time Canon user and I think Canon generally makes good gear, and there are some lenses like the RF 28-70 f/2 which if they suit your use case and budget would make Canon an obvious choice, but at least at the moment the Sony system would be a much better fit for my preferences.