The excellent Eigenclass blog had an interesting article on that once:
http://web.archive.org/web/20120126022146/http://eigenclass.org/R2/writings/object-size-ruby-ocaml
There also was a good discussion on ruby-talk, which led to some code by Robert Klemme (Ruby Best Practices):
http://www.ruby-forum.com/topic/156648
http://www.pastie.org/217131
Plugging the values from the first article into the script might get you started and is probably quite educational.
You could also check out memprof, though it's more about object references and finding memory leaks than actual sizes:
http://github.com/ice799/memprof