In the lineage which I am studying, we often do a form of Trikonasana in which the hand does not touch the floor at all. The focus is on keeping the spine straight, opening the heart, and feet are a bit closer together than in the Krishnamacharya -derived styles like Iyengar.

I am a certified Iyengar teacher. It is his teaching that all poses must be built from the foundation. So yes, you are correct that all of the side extended standing asanas have a connection to the ground in some manner. In this case, the foundation of Trikonasana is your legs - or the feet to be most specific. The feet and the legs direct the alignment in the pose. The hand is there to give you additional balance and extension. But it is the legs steering the body into the pose. The legs/feet are the rudder steering the ship -- if you will excuse the analogy.

In trikonsana, there is a tremendous amount of upperward lifting. While parts of the feet are pressed down, you should have the knees & quads lifting up, the chest extending up. Thus, the weight on the hand is very little. And, eventually, it would be even weight regardless of which side you were working on.

The hand should be placed high enough that you can get the feeling of extension, of height through the body. That means the fingers can be on block(s), chair or the leg. Often people can get their fingers the floor, but it is not recommended in the Iyengar system to go that far down until you have the understanding described above and the flexibility to demonstrate the understanding above. :)

PS This is my personal understanding of the Iyengar system. Don't take it as gospel until you have tried it yourself.

Its great that you are so mindful of this. How much weight did you find when you used the scale?