Do fuel canisters generally (ie under the same conditions re: water temp, wind, air temp etc) become less efficient as they become less full?

Additionally, if my stove takes 6 minutes to boil 2 cups water the first time I use a canister and uses 7g of fuel, is it reasonable to expect that it may take longer to boil 2 cups water but should take the same amount of fuel when the canister is near empty? Or would it take more fuel and thus more time to boil that last 2 cups?

Here's some of my thoughts:

the amount of energy to heat 40 degree water to 212 degrees, all other factors being equal, should remain the same. X grams of fuel will produce Y BTU's on a stove and thus raise the temperature to boiling using the same amount of fuel. However, does the fuel actually "escape the canister faster" and thus burns faster delivering more BTUs over a shorter period of time when the canister is full?