From commenter Coyote:

Back when this policy was new, I asked a screener, "volume or weight?" He said, "Huh?" I answered that "ounces" in English units were both a measure of volume and weight, and for most substances these two numbers would be different.

The screener looked more puzzled, but then eventually answered "volume." I believe this was the correct answer, because the rules talk of "3 oz containers" which only make sense in the context of volume.

So, having gotten the "volume" answer I expected (though with more puzzlement than I anticipated) I then pointed out that the toothpaste he was attempting to confiscate for the good of the Republic was actually measured in ounces of weight. The toothpaste was "net wt. 4 oz." So I Observed that the volume was much less than 4 ounces, so I should keep it.

After staring at me, and I think wondering if he could shoot me, the screener gave an answer right our of Spinal Tap: "But it says 4 ounces." (But it goes to 11!)

Anyway, I let him have my contraband toothpaste and moved on, not wishing to get detained or make the no-fly list. But it was absolutely clear that whoever crafted and disseminated the policy did not know the difference between weight and volume. I still to this day meet screeners who don't understand the difference. Though since then I have seen airlines amend their web sites to say "weight or volume" thought the department of Homeland security has never added any such clarification to their web site.