I actually found the opposite when I moved to a heavier camera, I found it suited me and it feels much more stable. I obtained (thanks Showipix) a monopod for when I use my 7D with the 70-200/2.8 which weighs in at 3.0 kgs, but I found that it is more a hinderance to me so I rarely use it. There is a lot more to the technique of holding a camera than a lot of people give credit for.
I found this video a while ago that might help you a little. He faffs about at times but the basics of centre of gravity, and getting your elbow in tight under you camera to get maximum stability is the key. There is also a bit of talk about slow shutter speeds (which doesn't sound like your issue here) that is good advice. Take from it what you can.
http://www.youtube.com/watch?v=EDsx3-FWfwk