I believe the "ton" ratings are leftovers from the WWII military. The military classified their vehicles by the ability they could haul for planning and logistics purposes.
So, during WWII there were the early Dodge WC series trucks that were 1/2 ton rated. Then later they upgraded to the 3/4 ton, the most well known of which was probably the WC-52, often called the "Weapons Carrier" (contrary to what some will tell you, "WC" does not stand for "Weapons Carrier", it is the Dodge model designation for their 4x4 military trucks made during WWII.) The WC series included the WC-52 (basically an open top pickup, early in the war it was nicknamed the "Beep."), the Command Car, which was an open topped passenger vehicle, and the "carryall" which can be thought of as the ancestor to the modern wagon-type SUV.
Here's a good Wiki article on the WC series:
https://en.wikipedia.org/wiki/Dodge_WC_series
Other manufacturers, of course, also made vehicles during WWII using the "ton" ratings to classify them including, of course, the GMC CCKW "Deuce-and-a-half" (2 1/2 ton truck) and the Willys and Ford "quarter ton" i.e the jeep.
With regard to the cargo carrying capacity being higher than the "ton" rating, when I was in the Army it was explained like this: The "ton" rating of the vehicle (for the military, at least) explains how much cargo the vehicle can carry OFF ROAD.
ON-ROAD the same vehicle could carry as much as twice the cargo capacity. So, IOW, a "deuce and a half" could carry 5 tons on the highway, but only 2 1/2 tons off road. Similarly, a Jeep could carry 1000lbs on the road but only 500 off road (hence the "quarter ton" designation.)
Since the early post-WWII pickup trucks were derived from the military trucks that were made during the war, they carried those "ton" designations with them. So the Military 3/4 ton became the Dodge Power Wagon and other manufacturers followed suit classifying their lightest trucks as "half tons", the next step up as "three quarter ton" and the next step from that (the largest of the "light duty" trucks" as "one ton" trucks, even though in reality a "half ton" truck could typically carry more than 1,000lbs and a "one ton" truck could typically carry more than one ton.
Be nice to ride dirt bikes/snow machines right out the front door.
