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That's about right. You can find the weight of your car by subtracting the weight capacity from GVWR which can be found on the driver's door. That'll give you the weight of your car with a full tank of gas. The DMV value most likely doesn't include gas.
OEMs provide weight data since some states use it for determining registration fees, but it's not always clear to me how this weight is determined.
Weight data is typically used to compute registration fees for trucks, but not too many states use it to compute car fees. It's somewhat of a legacy from the past like "taxable horsepower".
The "curb weight" of the '01 base Z06 is quoted by Chevrolet at 3126 pounds, if I recall correctly. Curb weight is the weight of the base vehicle with full fluids includiing fuel, and all normal equipment. Shipping weight is generally the weight of the vehicle with full fluids except fuel, which would only be three gallons, so the shipping weight of a Z06 would be curb weight minus about 90 pounds (15 gallons), which brings it down to 3036, so it looks like the 3044 pounds listed on your registration is Chevrolet's claimed shipping weight.