Nobody is talking about it but I believe it has been proven that the lightest practical cooking fuel/system is the Esbit/solid fuel cooking system. I'd do strictly Esbit if I knew it were readily available along the AT. There seems to be some contradictory information as to it's availability. I carry 2 tablets as a secondary cooking fuel in the case my primary should ever fail. It's also a very good fire starter and unused portions can be extinguished and re-lit.
The new folding Titanium Esbit stove (with pot stand) is .4 ounces, homemade foil windscreen .15 ounces and an Esbit tablet (enough to boil 2 cups of water) is .5 ounces. If you read a little, you'll find tips on how to extend the use of the tablets and keep clean up minimal. Buying in bulk and placing in your mail drops is a way to mitigate the cost. But then again, I don't believe cost has been introduced into the equation here as a major consideration.