I've noticed that Cookie Clicker has a really nasty memory leak, in the current version. I'm using Safari on OS X 10.13, everything newest version, on a 2015 MacBook Air, if any of that matters. I have all the "may affect performance" options turned off, and don't have Cookie Monster or any other enhancements active.
I've seen it climb up to more than 4GB of memory. I tried leaving it running overnight, and the browser window crashed because the memory climbed too high. I've tried saving the game and removing all local storage and data saved by Cookie Clicker then reloading it, no dice.
Right now I've got it running in the background, it's been maybe 10 or 15 minutes. I've only interacted enough to click a couple golden cookies. It's currently sitting at 1.16...no, just jumped to 1.37 GB of RAM.
There's not a ton going on, I'm only up to 408m CpS, so my computer should be able to handle it just fine.
If I can't leave it idling, I'm never gonna be able to click all these cookies!