I love to go on extended backcountry trips, foraging my greens and boiling my drinking water. I carry in dry lentils, some grains, cooking oil, salt, and some spices. Here's a low weight, small size, cheap way to cook:
(1) cook pot, preferably more fat than tall
(1) aluminum throw away pie plate
(3) aluminum tent pegs
(?) some twigs
(3) optional rocks
1. Place the pie plate on the ground (after clearing away highly flamable materials).
2. Pierce the three tent pegs through the pie plate and into the ground. Space them so as to make a sturdy stand for the cook pot. A fat pot works better as it is more stable, and more heat reaches the bottom of the pot (larger heated surface).
3. Place gathered twigs onto the pie plate inbetween and around the tent pegs.
5. Put pot on top of tent pegs.
If you are concerned about the heat on the ground, place three flat rocks under the pie plate to keep it off the ground. You can also use rocks under the pie plate to raise and lower it, effectively controlling the heat to the pot.
This method uses very little wood, keeping your fire small and concentrated closely on the cook pot. The smaller fire is easy to conceal, so long as you keep smoke to a minimum (material selection).
This method is leave no trace if you put rocks underneath as the ground does not even become warm. The ashes are kept on top of the pie plate, and can be stashed under a rock after cooking. Replace duff (ground debris) to cooking spot, disguise footprints and nobody will know a fire was burned there.
This design weighs a pie plate and a cook pot since you can use the tent pegs after they have cooled for a tent or tarp. There is no fuel to carry as adequate wood fuel (twigs, etc) can be found virtually anywhere (parking lot).
I used this setup with a travel partner every day for 4 months and the originally pie plate was still fine. Be careful about removing pie plate and pegs though if you want to continue with a bigger fire after you've finished cooking. They will eventually melt. My friend did this to my setup (what a dork).
If it starts to rain, just stash some twigs in your pack or under a rain cover. This will give you something to start with, and you can lean twigs up to the fire to dry them out. If you're really stuck, use hand sanitizer as an effective fire starter.
Once we could not find dry wood anywhere, and ran out of sufficient clean water. We walked back to civilization and got water and a little chemical water treatment kit, but never had to use it.
enjoy, this really works!