I would agree with Colin's method. I have laminated a number of pieces with excellent results. I'm not sure about creating entire sheets of 1/8" that way, but I don't doubt it can be done.
For example, I laminated a LE and TE set for a mid-sized I-beamer. The TE was 3/8" by 1/2" laminated from 3 pieces of 1/8". That results in two gluelines. The resulting TE stock was a bit over 43" so that I could trim it down for this elliptical wing.
The weight of the glued-up blank (no shaping or sanding) after fully drying was 20.0 grams; the prepared wood prior to glue-up was 19.1 grams. With proper control of the glue thinning the weight gain of this method is negligible. But don't expect to slather on full-strength Titebond, then add enough clamping pressure to balsa to achieve a proper glueline, and thus keep weight growth under control. That is not a viable method. You will crush the balsa trying to get there.*
As far as the warping, I clamped the TE to a piece of aluminum angle and let it fully dry. It is straight. Better than a single piece with one caveat--you will be sanding a glueline. With the thinned glue, this isn't near the "rubbery" experience you might be expecting. I didn't have a problem with it.
My suggestion would be to try a sample or two. Tune your methods up. See if you are happy with it.
Dave
*--there are also a lot of guys who will tell you that you can't use Titebond to glue plywood doublers to a profile fuselage. That it never dries. That the gooey mess will allow the fuselage to "let go" under engine vibration. That's nonsense. The issue is that there was extreme excess of glue used, that it was not thinned, so no reasonable amount of clamping was going to allow squeeze-out, and the moisture migration was going to take a long time. And by then, these guys might already have paint on it so where is that water going to go? When gluing things together, the methods make a huge difference in the results.