3/4 Ton 250, 2500 payload limitations (gas vs diesel)

To the OP a more direct answer, because a 250/2500 is a class 2 truck it has a max GVWR of 10,000#. Simple math says as curb weight goes up, payload will go down.
Why high tow ratings for the diesel, simple torque and HP.
The reason 250/2500 diesels exist is due to crazy licensing fees and some HOA rules.
Will a diesel carry the load, most 250/2500 are the same as a 350/3500 SRW, same engine and drive train, just making difference for the reasons stated above.