[edanm]

Usually what's looked at is average weight, since you're absolutely right - weight can fluctuate for many other reasons, including amount of water in your body. You can drink a liter of water before weighing yourself and weigh 1 liter more, though obviously that isn't anything we care about.

But if you're running a 1000kCal deficit for weeks, you are going to lose weight. Just think of the limit case - if you normally eat 3000kCal to be at maintenance, then running a 3000kCal deficit will cause you to lose weight quickly, then eventually die for lack of food. Eating at 3000kCal will cause your weight to stay the same. Deficits in between will cause you to lose weight more slowly.