The best ultralight stove is not so much an issue of the stove. More, it is an issue of the availability of fuel.
You can look at pressurized liquid stoves that burn variations of gasoline and kerosene. You can look at unpressurized liquid stoves that burn variations of alcohol. You can look at stoves that burn commercial solid fuel like Esbit. Then you can drift down into other fuels like wood twigs, wax, etc.
In most parts of the civilized world, there are petroleum fuels. Most gasoline mixtures are dangerously flammable, and you may not want to fool with them. Airlines won't let you check baggage or carry on baggage with them. You might be able to purchase fuel in each new location, or maybe not.
In most parts of the civilized world outside of Moslem countries, you can purchase alcohol. However, to be a good fuel, you generally need to get up to about 75% pure ethanol. Maybe methanol also. Alcohol is a crap shoot.
In most countries outside of the US, UK, maybe Canada, maybe Germany, and maybe a few others, it is very difficult to find Esbit fuel, so you might as well forget it.
Now you are back to the wood twigs and wax. Those are easy to transport, but not the most efficient fuels for a backpacker.
If I had to do this trip, I would take two stove systems in order to hedge my bets. I would take one good international-type multifuel pressurized liquid stove and one empty fuel bottle or maybe two. Then I would take a multifuel thing like a Trail Designs Ti-Tri Caldera Cone in order to burn wood twigs and wax. The Ti-Tri comes with a lightweight alcohol burner as well, and that would cover you for almost anything.
In Nepal, they collect yak dung from the fields and sun dry the patties. Then they burn that inside in a good stove.
–B.G.–