It is. That is, the difference between a full airplane and an empty airplane in terms of fuel burn is quite marginal, maybe even less than 1% net fuel burn. This is because how heavily an airplane is loaded does not change its drag coefficient. A heavily loaded aircraft will not climb as quickly as a lightly loaded aircraft, but for the airliner, that just means it gets to cruise altitude a minute or two later than it otherwise would.
The way to generate more lift is by increasing the wing's angle of attack on the wing (i.e. point the nose up). In addition to increased lift this also increases drag.
Actual numbers are hard to find, but considering the weight of a commercial aircraft can vary by as much as 50% between empty weight and maximum weight, I'd wager it is well over 1%.
