392Hemi,
This is referred to as stringing your crosses "one ahead".
This accomplishes two things... easier weaving and minimizing string to string friction.
First, the actual weaving of each cross is easier (because you are going through "soft weaves" rather than "hard weaves").
Example: if you're currently weaving the 7th cross, the last cross actually tensioned is the 5th cross. This makes the 7th cross easier to weave, because the mains are still oriented as a "soft weave" from the tension that the 5th cross is applying to the mains.
Now... had you tensioned the 6th cross before weaving that 7th cross, you would have just created a "hard weave" for yourself, instead of the nice "soft weave" that occurs by delaying the tensioning of the 6th cross (until after you have woven and fanned almost all of the string for that 7th cross).
Once that is done, you can then apply tension to the 6th cross, clamp it, release tension from the gripper, pull the remaining bit of slack through, and move on to weave the 8th cross (which will now be easier because of the tension the 6th cross is now applying to the mains).
Rinse and repeat... tension 7th, weave 9th, etc.
Secondly, since you are weaving and fanning each time, through mains that are oriented as a "soft weave", there is much less friction (wear) on all of the strings (crosses and mains).