All browsers blow up in size, especially when you plan to use extensions.
Portable browsers often store (part of) their cache in a folder inside their main folder. So i would purge the cache first and see how much storage space is being cleared up.
If storage space is an essential requirement, disable cache entirely. But that will affect your browsing the internet. in lots of ways.
Buying a bigger HD or other storage device should not break the bank. In case of a hard disk in a laptop or desktop, you can pretty simple clone the old hard disk onto the new one.
Diverting cache folders onto a portable HD could be an option (if that portable HD remains connected).
And if another storage device isn't an option either, delete stuff from it that you don't need. Or move stuff that you haven't opened in 6 months or more onto a (marked) dedicated pendrive or portable HD.