The weft weaving starts in one corner, attaching the a doubled cord (roughly 120ft length folded in half) at its center onto a side rail.  This is where I should have tacked it in place prior to the final wraps over the rail.  It's no big deal, it will never be seen unless someone peeks underneath. 
The weaving starts with a wrap around the stretcher, catching the pigtail that's the end of the rail wrapping.

The first row butts up against the cow hitch loops on the rail.  The entire 60ft of doubled cord has to be pulled through because the weft strands make their turn at the other end by circling the far stretcher.  This slowly gets more and more difficult as the weft moves across the bench and the warp cords tighten up.  You kind of get into a rhythm, though. 

From underneath, you can see the pigtail slowly getting concealed under the stretcher wraps.

And that's what 120ft of cord fills in.  There's some wasted cord because there's only one good place to hide the knot that joins the next 120ft of cord, which is under the wide center band of warp cords.

This is nearing the end of the 2nd length of cord.  Why not use a single longer piece of cord and do the full seat in one go?  The problem is that pulling that much cord back and forth through the warp cords would be more work.  And the longer the cords, the more likely they'll get tangled as they pile-up on the floor when you're pulling it through.  (and there's already a generous amount of tangling to deal with shorter lengths)

On the center wide band, I wanted to mimic the pattern that's on the back of the Wegner CH-25 chair, which catches the inner 4 strands on one pass and the pair of outer 2 strands on the next, before returning a full 8 over/under pattern.  I found that I had made the center warp cords a little too tight to make that pattern in a tidy way, so I just caught the inner 4 before returning to the normal pattern.  It still provides some visual interest to the center band.  There will be 3 of these when I'm done.

Time to join another length of cord. 

I'm using the knot that Caleb James recommended in his weaving article in Popular Woodworking.  The working ends of the last cords are passed through the loop in the next length, one end is wrapped behind and around to the other end, and the pair of ends get an overhand knot.  It's kind of a chunky knot with Danish cord, but it all fits under the center band of warp cords.

I left a couple inches of the trimmed ends in place in case I needed to adjust something.  I can trim them off later from underneath if needed.  The center stretcher conceals the knots on the underside somewhat.

Getting closer.   

Finished! Well, all except going back to tug the warp cords around so they're straight and perpendicular to the sides. 
I estimate that it took close to 800ft of cord to complete.

I moved it out of the messy workshop to stake my claim on the inaugural sit test of the finished bench.  Feels good to me!