Oh, you've raised a few more good topics here.
Yes, TIFF files sure can be big, but it's very possible that yours were bigger than they needed to be. Do you happen to still have one of those TIFF files, easily accessible? If so, could you send it to me? I'd be interested to take a look.
Well, there's a good argument for NOT keeping tiff files for archiving. Once you've finished the job, and are about to put it onto an external (or cloud, or whatever), it's quite logical to convert the tiffs to jpegs for that purpose. I talk about this in some detail in the Bridge Class.
Tiff files, or PSD files, are so important while a job is live. But if space is an issue, you certainly can consider converting to jpeg for archiving.
Having said that, thankfully disk space is becoming much cheaper with each passing year, so it's not as big a deal as it used to be.