Stove choice depends heavily on application and personal preference. There are some white gas and canister stoves which are great cookers (have a good range of adjustment for simmering), but weigh quite a lot. Similarly, there are some canister stoves that are fast boilers, but weigh even more. The lightest canister stoves tend to be slower, less fuel efficient, and less wind resistant for boiling water, but the difference in weight of fuel carried due to this is rarely noticeable.
Alcohol stoves are the lightest, but since the fuel doesn't burn very hot, a lot of alcohol must be carried for longer trips, which can outweigh (literally) the weight saved over canister and white gas stoves. Alcohol stoves are also the least wind resistant and slowest to boil. However, for shorter trips (4 days or less), they are indeed the lightest option. For overnighters, there's no beating them on weight.
For trips with more than 5 days in between re-supply, I'd go with a white gas stove or canister stove, as they are lighter than alcohol when carrying fuel for this much time. Additionally, they perform better in cold, wind, and in general. However, keep in mind that even on longer trips, if your re-supply period will be less than 5 days or so, alcohol stoves make a lot of sense: you can buy more stove fuel at just about any gas station, convenience store or hardware store. Although the more expensive white gas stoves let you use gasoline and kerosene, alcohol stoves still have the advantage of having no parts to break (and even if one does break, you can improvise a new one out of some garbage using your pocket knife). By contrast, I've had a white gas stove break on me more than once. Something like that could surely complicate a long distance hike.
I've used alcohol stoves seriously for backpacking in the past two years and have only missed canister stoves in colder weather, when they are very slow to boil. For this problem, I recently picked up a Vargo JetTi because it's supposedly the lightest canister stove at 2.7 ounces (2.9 on my scale), and I like the way the potholder packs down; however I just got it today and haven't gotten a chance to use it yet, so I'll withhold my recommendation.