Definition: Single weight （單重) is to have all or most of one's weight on one foot whereas double weight (雙重) is with one's weight evenly distributed on both feet. The classics said single weight is preferred to double weight.
I just read a recent post of Wu-style sifu Jim Roach's Classical Tai Chi Blog with the title: The true cause of "double weighting". An old issue revisited. My contention is that such debate is totally unnecessary, as I shall explain below.
The issue of single vs double weight has been a "classic" debate between practitioners of Yang style and Wu style tai-chi. Essentially Yang style is medium to long stance, making a practitioner's best stance as 70/30 weight distribution; and Wu style is short stance, making a practitioner's best stance as 100/0. Sifu Jim Roach explained clearly that in combat situation a 100/0 stance with ease of shifting the weight between the feet can give a practitioner an advantage of mobility and faster reaction time. In addition, since a Tai-chi practitioner can easily transfer his weight through subtle energy transfer in his core (dantian), his opponent will find it difficult to determine his weighted foot (it is interesting here to compare seasoned practitioners of "external" martial artists, like professional boxers, who can be seen to shift his weight constantly from left to right, front to back. And the same can be seen in sports, like tennis, where mobility is an important success factor).
Anyway this is combat. But work-out or training follows a slightly different route. It is interesting to see that Sifu Roach actually "complained" that some of his students (probably with previous Yang-style training) said Roach's stance was "double weighted" and tried to correct him! This I must give credit to Roach because he can truly disguise his dominant weight.
But training is different. In the classic Wu-style as taught by Grandmaster Wu JianQuan 吳鋻全, a practitioner must have stance (short-stance) in such a way that it can be perceived by anyone as 100/0. That means in the forward stance (功) the spinal cord should be at an angle to the horizon (which Yang style practitioner will sometimes laugh at!), where in a backward stance (座)， like all Tai-chi style, the front foot will be tilted upwards. For all intents and purposes, these are stances for work-out rather than combat! Understanding combat requirement is important, but using such requirement to credit or discredit a work-out system will be totally irrelevant!
Taking the issue of combat aside, a long-stance of Yang-style does have an advantage of training the strength of one's leg muscles as well as requiring to opening up more one's pelvic joints. But of course, training one leg muscles and opening ones' pelvic joints (groin 胯) require other specialized training method other than, or in addition to, doing the Form.
And I rest my case.