Dropbox may seem like it doesn't need a lot of RAM to operate. The truth is: there's a lot of complexity under the hood!
For instance, Dropbox has to keep track of a lot of information about your files in order to make sure it can sync files quickly and efficiently. The more files you have in your Dropbox folder, the more memory Dropbox will need to keep track of them. That said, we are constantly working on making Dropbox more memory efficient and we continue to have significant improvements with each major release.