I am seeeking a better understanding of the fault, single and double floating.

I don't understand. What are you asking.

It is in reference to Yang Style Tai Chi , my research turned it up in a book regarding their family secrets. For example, one I better understand is "Double weighting" in reference to Shaolin as compared to Tai Chi where they teach that equal weighting of both legs results in loss of speed of mobility as compared to the power of Tai Chi in shifting weight.
I'm asking this question because I don't understand what floating is?

Floating is unweighting . . .

In kenpo, for example, floating is used to maximize the amount of travel on a downward strike. In a technique against a left lapel grab where the attacker is about to punch with his right . . . I execute a right front kick to the attacker's rear knee at the same time as I execute a blocking right punch. I then float up on the ball of my left foot and drop my right elbow onto the arm of the attacker.

This is only part of the technique and it is the first time I've tried to explain a technique in my own words.

Have you ever been snow skiing? You float or unweight to make parallel turns.

I think it is because it's vague movement from an unrooted base and lacks sensitivity. He is making the distinction between lightness and sensitivity and floating without sensitivity.

Seems to be an extra un-needed step. I don't understand how rising your center in an uncontrolled situation is helpful. Can anyone tell me the benefit to this. I understand the worth in dropping weight with technique and all, but it seems that something else may be more effective. Just an opinion. you tell me.

Niahanchi kata is supposed to teach floating.. based upon center of gravity, to not be stuck in a static position/stance... to be able to move, in essence to control you center of gravity.

Frank