Usually I save TIFFs until I print or I'm able to reallylook at the page and make sure there are no errors in my journaling or my dates/locations (I tend to change some info for LOs I post online, so I have to make sure my full-size LOs are correct). But having said that, I still don't save all my LOs. I can remake a page, and I started DSing like 2007/2008: I don't need TIFFs for LOs that are a decade old...I'm not going to print those now, tbh lol, so why save the TIFF?
As for BB: they take care of big files once every 48 hours.
Here's info from their website. There's a link on that page to their "How to exclude files" help page, which could help you speed up your backup IF you're comfortable not backing up these PSD files. Oh, and you may already know this, but if you want you can set up BB to email you if your computer or EHD hasn't been backed up in a certain amount of days. That has saved me a few times when I've unplugged an EHD and totally forgot to re-plug it in.