As a young'n I was taught the Waking Kata. From the very beginning we heard "yoi" which was our command to rise up on the balls of our feet. As I recall we were taught that you should be able to slide a piece of paper between your heel and the floor. The entire kata, indeed the entire art form was to be practiced this way.
At this point of my development I would like to challenge this idea of constantly floating on the balls of the feet. The first point I would like to point out about riding the balls of the feet is this required the calf muscles to be firing constantly. In my humble opinion muscle tension just to remain standing is inefficient. Second, riding the balls of the feet causes "floating" to happen much easier. Floating is a balance break when your weight shifts forward and you become pinned on the balls of the feet as a result from body rise.
The New Idea - How to distribute weight on the feet
Stand normally and relaxed on your feet. Now focus approximately 60 percent of your weight on the balls of the feet, and let the remaining 40 percent dissipate through the rest of your foot. Your can keep weight on the heel. Just make sure more weight is on the ball.
This is how the foot works. Don't reinvent the wheel...er..foot.
Why not use your entire foot? It is natural, the way we were evolved to walk. We can through training make it more efficient. The old way of focusing your weight solely on the balls of your feet means you are balancing your entire system on two points, one per each foot. The human foot was evolved to carry weight on three points per foot! 1 versus 3. Which sounds more stable?
How weight is normally distributed.
Look at he above picture. For Aikido purposes switch the focus of weight (most weight) from the heel to the ball. Switch the (second most weight) to the heel, Otherwise this picture stands as a good example of what we should be doing to be relaxed dynamic and NATURAL.
Try the old way too, and use what works for you and your practice.