I tend to try to wean between 6-7.5 weeks. Like others have said already, it really depends on how the doe's condition is. When I was using a feed with too little fat, they had to be weaned earlier. Once I started adding enough fat to the diet, the does have held condition very well even with a later weaning. I am very happy about that! My does usually like cuddling and hiding under their kits for as long as they have them. Sometimes a first-time doe will want some space, but that is usually only when the doe had a litter of 10+ kits and they are getting crowded in there! Oh, I also wean based on litter size and the individual kit's weights. I don't want a cramped cage, nor do I want smaller kits going to their own cage yet.
My does tend to stay in full milk all the way up to weaning. Because of that, I try to wean the kits over a period of a week if possible, sometimes more. Usually I check to see which gender there are more of. Then, I take the three largest kits of that gender and put them in their own cage. The next day I'll take around three more, depending on the litter size, and add them to the cage (that might be moving three of the other gender to their own cage, though). I gradually remove the other ones, sometimes leaving only one-two for the last day or two. I always want three kits moved into an empty cage, since they seem to relax much better with three than with two (and in the cold weather, three is better for warmth).
When the kits are moved to their new cages, they get excited about establishing their new hierarchy. Usually one is going to pester the others by mounting them for the first while and having three makes it so one of them is left alone at least some of the time!
To sum up- I move them out gradually and put them in cages separated by gender.