I agree that the LIGHTEST stove is the Firelite Ti wing stove for ESBIT tabs. I carry it as an emergency stove & as a backup for my canister stove if I miscalculate how many canisters to bring.
FORGET THE SCRIPT BELOW: I now have a Caldera Cone ti Sidewinder stove. In ESBIT mode I use the outer cone, a tiny ESBIT tab holder called a Gram Cracker and a small 2" X 2" aluminum base sheet. My Sidewinder was ordered to fit Trail Designs' 3 cup aluminum pot (hard anodized). Not the lightest ESBIT stove but certainly the most efficient. I now use 1/3 less fuel than with the setup described below due to the Cone's efficiency. Now THERE'S some weight savings for you, less fuel to carry.
BUT, I also own the Vargo Outdoors Triad XE titanium stove.
It's a "multifuel" stove in that it can burn both alcohol and ESBIT fuel tabs. In fact it can burn TWO ESBIT tabs side by side if you need more heat in a hurry.
It weighs 1.5 oz. That's right, 1.5 oz.
It costs $32. and is very well made. The alcohol burner has a removable lid for easy filling and a nice, efficient flame pattern. That's the stove I'd recommend to you. Personally I favor ESBIT tabs over alcohol for many reasons. Their only drawback is a brown film they leave in the bottom of a pot, which, BTW, is easily wiped off.
HOWSOMEVER, as was previously pointed out, your beer can is inefficient (too much heat goes up the sides). You need a wider pot. Bite the bullet and get a 1 liter aluminum pot and lid.
Otherwise, if you stick to your old beer can you'll have to carry more fuel to make up for its inefficiency. This is simple physics and we all had to come to terms with it.
Oh yeah, windscreen. I almost forgot.
I got an MSR windscreen kit B/C it was convenient. It has an aluminum reflector disc too. I use the disc under my Wing or Triad XE stove. I punched 1/4" holes about 1 1/2" apart around the bottom of my windscreen for better updraft.
You can, for less money, get a long disposable aluminum baking pan & make a windscreen from it as well. Don't forget the reflector disc. It's a fire safety item also.