We're all familiar with this concept from having to do "heavy object lift" tests and the good ol' "ball bounce" but what weight and balance really do for your poses is give them a sense of "believability". One of the gifts we have in animation is the boarderless playground of our imagination to create whatever characters and worlds we can dream up. However, in order to get our audience to believe in the products of our imagination we have to give them credibility. No matter how caricatured you are working, weight and balance should always come into play or there will be something about your work that will look odd, wrong, or worse yet....unbelievable.
Take a look at this pose from Frank Thomas of the woman and Merlin squirrels from "Sword in the Stone".
The female squirrel has a great sense of weight (and I'm not talking about her size). Her sense of being off balance is reinforced by the Merlin squirrel leaning in opposition against her. You can see by the use of straights and angles in the arms the tension and strain of Merlin trying to hold up the other squirrel.
Last year I had taken my family to see a performance of chinese acrobats. Beyond the amazing and entertaing feats of physical discipline, I was fascinated by studying how they carried their weight. No matter how fantastic the pose, the heads of the performers (unless balanced by a wider stance) was always in a direct plumb over the weight bearing foot. This idea of weight and balance should also apply to the physics of your animation as well as your poses. Keep Sir Isaac's laws in the back of your brain when posing and working on the physics of your movement. You can have a character with 8 legs walking on a planet made of spounge cake, but does it have a believable presence in the space it's occupying? That's where wieght and balance help the audience connect with your work.
Law and logic clearly prove to me that a coyote cannot ski down a hill with a refrigerator on it's back. However, if you show me an entertaining and believable pose....you can probably talk me into it.