I think I made progress as to why it takes up so much memory! When I went into Task Manager and clicked on the little arrow so I could see which processes were running with RStudio I saw that RStudio kept creating "git for windows" processes which rapidly took up a lot of memory. This must surely be related to the problem, right?
To answer your questions, I have tried resetting RStudio's state and I'm not working with files/packages located on a networked filesystem.