I know everybody sticks to the high dollar equipment...but..
years ago I used a "scout Tent" .. it was just a regular A frame.
easy setup.. inexpensive..and light...
I just pulled it out not long ago... put it on the scale...2.5 lbs.
I see almost the same tent on the internet.
Stansport Scout Backpack Tent.....for about $30..
it says it weighs 3.8 lbs... but I bet you remove the poles and use your hiking poles you can drop that weight...
anyway... just an idea..