Weekly losses depend on how much you weigh at the outset, and on how you as an individual metabolise food, particularly carbs. During the two week Induction period losses can be amazingly high - 10 pounds or more, but they can also be much less, particularly if you have been dieting for some time before starting Atkins. The high initial losses are mostly water, as they are on any diet.
I would think that the average weight loss on Atkins is 1-3 pounds per week. Some lose a lot more, others, less. Sticking to the rules is vital to get the best results.
I love Atkins. All the best if you decide to give it a go.