I'm thinking you posted in the wrong forum, unless you are built like Gronkowski or JJ Watt- hauling a 34 pound cot/tent is going to be quite a feat with a backpack.
If truly a backpacking element to it look into a bivy, tons of options, here's a place to start
http://www.backcountry.com/bivy-sackshttps://www.bigagnes.com/Products/Detail/Tent/ThreeWireBivySack ---- less than 2 pounds