Found this web page when surfing google for "single weighted".
It is titled:
A STUDY OF TAIJI PUSH-HANDS
Here's the link, if anyone cares to follow it, there is a good amount of info here as well:http://www.nardis.com/~twchan/ph.html
Here's a cut from that page:
Chen Xin, a writer from Chen Village (Henan Province, Wenxian County), has an excellent way of speaking about push-hands in his Taijiquan treatises: "My spirit allows me to know what is coming. My wisdom allows me to hide the attack." "Spirit" simply means using the nerves of the hands to feel the posture that the opponent is about to manifest. Then, according to my own wise strategy, I conceal an attack. In this way we arrive at the realm of "People do not know me. I alone know others." There is another saying, "If you are single weighted, then you can be responsive. If you are double weighted, then you are stagnant." In the practice of push-hands, it is most important to pay attention to these two sentences. You must at all times, in every moment, use your practical experience to really understand this. If you don't know this theory, then you cannot say that you know Taijiquan; you have only had a superficial impression. And if you don't spend several years in diligent practice of push-hands, you cannot speak of "applying technique according to circumstance". The interpretation of these two sentences is actually just common-sense and very easy to comprehend. Above, we have said, "The body is like a wheel. The waist is like the axle." Consider a wheel resting on the ground. Where can there be two heavy places? If there are two, then it cannot move, Therefore the Taijiquan Treatise says, "Do not allow any breaks or deficiencies; do not allow hollows or projections." The reason is that if there are breaks or deficiencies, hollows or projections, then you cannot be circular. And if you are not circular, then you will be double weighted.
Some people explain double weighted as both feet touching the ground at the same time or both hands striking at the same time. Thus, one hand and one foot means single weighted. This explanation is the worst kind of misunderstanding. We should understand that single weighted or double-weighted is not a matter of outer appearance but of the inside. Taijiquan is only the exercise of a central pivot. When you have found where this pivot is located, then your feeling will become spherical and every place will be single weighted, If you do not find the center of gravity, then your feeling will become stagnant and every place will be double-weighted. And it is not only the feet and hands--even one finger will be double weighted.
There is a desirable condition out there known as "single weighted", though apparently it has different meanings to different styles and even can mean many different things in any one style.
It's too bad there's no way to write a definitive "Tai Chi Chuan Dictionary" that everyone would use. Unfortunately people would never agree on definitions.
Anyway, I had a few minutes and decided to do a google search on the flip side of this coin to see where I got. This was the first page I found that was TCC related, there may be others, I'll keep looking.
[This message has been edited by Wushuer (edited 03-27-2003).]