You can back up all your data to iCloud but not the operating system or applications. The purpose of iCloud for the Mac isn’t backing up, its to make your data available anywhere you have access to the internet and for easy sharing. And the way iCloud works it isn’t really a good idea to try and store data there and remove it from your computer. There is simply too much risk of losing data completely. To back up your computer you really need to purchase an external hard drive and use TimeMachine.
If your MBA is the 13” model it has a built in SD card reader so that can be used to store data that won’t fit on the computer’s internal drive. Another option is to look at OWC’s SSD upgrade options.