The backup process is more than just moving files especially if you are storing tar.gz backups. The archiving and compressing are most cpu intensive tasks which can take quite a while to gather, archive and compress user files.
One way to save some processing is using incremental backups. This will only modify files that have changed but this does require more disk space as it is not archived and compressed.
Selecting Weekly backup will give you monthly as well unless you choose not to retain them below.)
Sounds like you've not configured it as you'd like. And if you were to check out this link, CPU/Memory/MySQL Usage you might see that gzip is whats causing server load during backup as it compresses your files.
Lot's to learn using cPanel. And lots of good Info on these forums. Most problems you'll come across, someones been there before you and there's a thread here somewhere that'll help you understand more about them.