from looking at Jeffs page the biner would do damage to the tree. I thought that was a no-no.
There's really not much pressure of the biner against the tree. Most of the force in on the part of the strap that goes around the back of the tree.
I will probably drop the biners in the future just to save weight and use the through-the-loop method lVleph is talking about.
Jeff says (I think he does, anyway) that if you're worried about the 'biner doing damage, you could wrap the straps around a few times, and rest the 'biner on the straps. Certainly wouldn't want to do something to harm the trees.
All of your weight talk got me worried. I checked and my descending rings from mountaingear.com weigh .4oz each or 1.6oz total. The same ish as yours.
A side story on weight, I contacted my local outfitter to see if they had a biner that would be the same as the nano one. I try to buy locally when I can plus they are only 10 minutes away. I told him my weight/force needs and that it was for my hiking setup. The best he could do was one for 2oz. 2 of them would added 2 oz and doubled the weight of the biners in my setup. He said," its only 2oz." He was kind of surprised when I told him yeah but 2 here and 2 there add up to pounds pretty quickly.
A side note that the people working there help you the best they can. But they don't always know what is best for you. After all none of them use hammocks or make any of their own gear.
Most of the force is on the back of the strap opposite the hammock. I don't think the biner would be putting much on the tree.