I've been following our friend Yukio's alcohol burners. Then I saw one of their video clips from a 2 gram alcohol burner. You say "Two Grams? Ha!"
Well, I whipped one out. It isn't particularly neat, but I figure it would get beaten up a bit from use, anyway.
The alcohol burner weighs 1.9 grams, and the windscreen/support is another 1.9 grams. Obviously, it is not going to boil a big pot of water, nor is the support going to hold up a big pot of water. So, there is some work here to make this more practical. I boiled 6 ounces of water in a recycled aluminum bean dip can. The burner was rather slow to bloom, but once it got going, the flames filled much of the windscreen (which I had sized to support the aluminum cup). I can probably speed up the bloom by putting an insulator underneath the burner.
Anybody should be able to make one of these, and perhaps make it better. I used two aluminum tealight candle containers, plus a narrow strip of Foster's can aluminum on the inside to make the low pressure vessel, plus a few drops of JB Weld. The windscreen support is just a wide strip of Foster's can aluminum punched full of holes. You might be able to beat the weight using hardware cloth for the support.
Ordinary hand tools, a nibbling tool, a pin, and minor stuff.
Edit: If you look into the center hole, you can just barely see the low pressure wall.