Before taking any measurements, I decided it was only fair to ask Nabisco upon precisely what basis they make their claim of "double." I mean, I didn't want to be comparing masses if "double" refers to volume. After receiving what might possibly be the least helpful email in the history of customer service (salient quotation: "Double Stuf just means that the cookies have a double dollop of the creme filling."), I decided that mass was the most likely definitive measure.
On the altar (dining room table) of science: one package standard Oreo cookies, one package Double Stufs, one Flinn Scientific OB2057 digital scale (accurate to ± 0.05g), one research assistant (girlfriend) with iPad.
30 carefully excised Double Stuf cremes 
We removed the cremey centers of 30 cookies of each variety and recorded them in a spreadsheet. I then multiplied each Double Stuf creme mass by 0.5 and recorded those values as well. (If you want to do your own science, here is the raw data.)
Now, if Double Stufs truly are (stuf x 2), then there should be no statistical difference between a stuf and a (double stuf x 0.5). Here are the results, courtesy of The R Project for Statistical Computing:
The single cremes had a mean mass of 3.27 g with variance of 0.009 g.
The halfdouble cremes had a mean mass of 3.27 g with variance of 0.005 g.
The kernel densities for the single and halfdouble masses are as follows:
Comparing the means:
In other words, if there is truly no difference in the two means, we'd expect to see a discrepancy this "large" about 50% of the time. In fact, if we ignore the question of direction and just test to see whether the two means are at all different:
A pvalue of 1! The means are so close that, after rounding errors, the results aren't statistically different at any level of significance.
I am officially convinced that Double Stuf Oreos are, in a sensible and meaningful way, doubly stuffed. The weird discrepancies in caloric info still remain to be explained, but not by me. I have trisected my last Oreo in the name of consumer protection.
Special thanks to the St. Louis Park H.S. science department for loaning an expensive piece of equipment to a crazy math teacher basically without question, and to Jenny Magdal in particular, who twice reminded me not to poison myself ("Seriously, please don't eat anything after you weigh it."). And, of course, thanks to my lovely assistant/girlfriend Dani for giving up an hour of her Saturday in the name of cookie inference.
