Origin of names half-ton, one-ton, deuce and a half, etc.

[davepl]

What did these things mean initially? I assumed when I was a kid it had something to do with cargo capacity, but 1000lbs isn't much. Maybe that's all a 1/2 ton pickup can carry?

Then I thought maybe it was the weight of the frame, an indication of structural capacity, but not likely.

If you know, let me know, and how you know (I already have the 'thought that when I was a kid' and 'Dad always told me that' answers sewn up, looking for something more authoritative).