"begin rant"
What the hell am I supposed to do with this!? Yes, Safari I’m sure that the page is using a lot of memory, but what would you have me do? Every time I load the page, you throw this message, and there is absolutely nothing I can do about it, other than not visit the page or use another browser. Stop taking up valuable space on my screen! I can’t quit the browser or close the damned window every 3 minutes. Ugh.
"end rant"
I’ve had that notice on one website consistently for some time, but since Big Sur I’ve had that issue across multiple sites. Safari was hogging ram like crazy (6+GB with just a single website open). I think it’s related to 1Blocker in some way. Turned off the 1Blocker button (per a suggestion on another forum from the developer) and its calmed down.
Ah, very interesting! I do have 1Blocker, so I’ll play around with it, and see what I get. However, I 1Blocker installed for a reason, and as I hate being advertised to and tracked. 
I don’t use 1Blocker, and I get that cheery little message when I connect to nfl.com (which, admittedly, is a horrible, cpu-gobbling website). I’m still on Catalina, FWIW.
As @jec0047 suggests, the problem almost surely is horribly-coded cpu-gobbling websites. Intrusive animated ads and gratuitous video and sound content waste bandwidth, memory and cpu resources.
I have stumbled upon a useful test to determine which websites to avoid permanently. I simply access the suspect website on my old 2010 MacBook Air running macOS High Sierra, then listen for the fan to start up. Those websites that activate the MacBook’s fan are banned - I enter the URL in the blocked domain list in my home network’s OpenDNS account.
Maybe Safari’s warning is a gentle nudge to avoid the offending website. That works for me.
I believe this is exactly correct. Unfortunately, as @TallTrees pointed out, it’s not always possible.
I’ve disabled 1Blocker, and it’s made zero difference. I then reenabled 1Blocker, and it’s not blocking anything on the site. I do wonder if Safari itself is blocking some of the content, and perhaps causing the issues. I don’t have the memory complaint issue/problem when I use Brave. It completely works as expected, but isn’t Safari.
I doubt this very much. Blocking content takes very little CPU.
The complaint is definitely coming from Safari. Brave supposedly blocks tracking but AFAIK not content. This would seem to suggest that the website is trying to track you VERY aggressively. But it could be something else entirely.
I’ve been giving serious thought to making Brave my default browser. Maybe you might want to consider the same (at least until Brave sells out 
)?
You can just remove the button and leave the rules. That alone has worked for me.
Interesting. For me just disabling the button has eliminated the issue so far. I’ve been running all day as normal and safari never goes above 2gb. I did try brave and had no issue so for me at least some combo of safari and 1Blocker appears to be it.
