Hot water in a soda bottle is the primary reason to carry a stove at all in snow country for some of us.
Otherwise we follow a no-cook strategy.
As a side note, instant mashed potatos hold heat even better than water though you would want to have them in a ziplock container rather than your bottle.
Gatorade and aquafina type bottles work fine as hot water bottles but just make sure it's HOT water and not ridiculously "hot to the point of melting the plastic" water.
In practice it is pretty simple to have your stove set up just outside your shelter and ready to go for a quick liter of hot water in the middle of a cold night.
As for fuel weight; if the intention is only to make hot, and not boiling, water you will find that a fraction of an ounce of alcohol or of an esbit tablet will do the trick.
I know there are those folks out there that say they have melted soda bottles using this technique.. Well, don't use boiling water.. Just hot water right?
As previously stated, this is probably best used as a suplement to comfort rather than a replacement for true insulation value.