Firefox seems to need more memory when I have it open for a long time and surf to many different websites. I was never able to find out why it behaved this way and assumed that it was either a memory leak or an extension which would be responsible for this behavior.
It seems that my assumption was wrong. Firefox saves the last 50 visited websites of a single session in memory which means that it could add up quickly if you visit lots of content filled websites. The reason behind this is that it is faster to access a already visited website if it still resides in memory instead of loading it from disk cache or from the server.