There is an answer here:
http://stackoverflow.com/questions/1248302/javascript-object-size[
^] - but it doubt it will be of any real use to you.
The problem is that Javascript is an interpreted language, which is implemented differently by each of the browser writers, and which runs in a world where memory usage is pretty much irrelevant. There is absolutely no guarantee that an object will take up the same amount of space for the same page in two different browsers, or even two different versions of the same browser - it isn't a useful metric by any definition of the term!