How do I attach the back of sheets of paper when layflat binding a book?
I don't know if there's a "standard" glue for this, but I would try rubber cement (regular solvent-based type, not water-based).  It doesn't warp the paper like water-based glues, and doesn't leave chunks like glue sticks can do.  The layer dries to a small fraction of the thickness applied, so variations in application thickness aren't visible.  With two sheets of heavy paper glued together, it won't be brittle when pages bend in handling.

Brushing it on the normal way holds paper well, but the paper can be easily separated.  There's a stronger way to apply it.  Brush a thin coat on both sheets and let it dry without joining the sheets.  Then brush another, thicker coat onto one of the sheets and while it is still wet, carefully align and join the sheets starting at one edge.  If you join them while the glue is still wet, you may have a brief ability to adjust the alignment a little if it's off.  If you wait for the second layer to dry before joining the sheets, it will be like contact cement -- the alignment will remain the way you joined them.  

It wouldn't hurt to immediately press the sandwich between two flat surfaces without shifting them (it doesn't need much pressure, and just a couple of minutes; putting the page in a cardstock folder like used for hot lamination will help avoid accidentally shifting one sheet when you press them).  Give the page maybe an hour for all of the rubber cement to thoroughly dry before working with it.  If any excess is pushed out, it will easily rub off when dry.

This "two coat" method gives a pretty secure, permanent bond.  The sheets won't peel apart in normal handling, especially if they're well-aligned so one sheet doesn't have an exposed edge to catch.  Current formulations of rubber cement are acid-free and have archival life.