Really depends if you've had your big first week, and how far from goal you are.... for example;
Person #1 is 9 stone away from goal and only joined weightwatchers; its very likely that they would lose a stone within 2 or 3 weeks.
Person #2 is about 3 stone away from goal and new to weightwatchers; they could very well get a nice 3-6lb kick start but its likely that the rest will be a steady 1-2lbs a week, so maybe 10-12 weeks
Person #3 is 1.5 stone away from goal... they've been chipping away at the pounds for a few weeks already, so the could take as much as 2-4 months..
The closer you get to goal, the more it takes to lose, the less your body wants to drop its fat reserves. It's always important to keep checking what points you are on is correct! Very easy mistake to make.
Also as someone mentioned, it really depends how honest you are being with yourself with your points. Estimations should be a rare part of your diary and you should log BEFORE you eat.