OP, take a look at the Owner's Manual. Page 4-50 lists a C2500 with towing capacities as follow:
3.42 6,000 lbs. (2 724 kg)
3.73 7,000 lbs. (3 178 kg)
4.10 8,000 Ibs. (3 632 kg)
http://assets.gm.com/manuals/chevrolet/1996_chevrolet_1500_owners.pdf
Check your glovebox for the RPO code for the axle ratio. Looks like at worst case, you have enough truck.
From the manual:
"Weight of the Trailer
How heavy can a trailer safely be?
It depends on how you plan to use your rig. For example, speed, altitude, road grades, outside temperature and how much your vehicle is used to pull a trailer are all important. And, it can also depend on any special equipment that you have on your vehicle.
Use one of the following charts to determine how much your vehicle can weigh, based upon your vehicle model and options.
Maximum trailer weight is calculated assuming the driver and one passenger are in the tow vehicle and it has all the required trailering equipment. The weight of additional optional equipment, passengers and cargo in the tow vehicle must be subtracted from the maximum trailer weight.
Above the 2,000 lbs. (908 kg) trailer rating, the engine oil cooler is required on C/K- 1500 models with gas engines and C/K-2500 models with gas engines and 3.73 (or lower) axle ratio.
Above the 4,000 lbs. (1 800 kg) trailer rating, heavy-duty or gas shock absorbers are required on C- 1500 models, and heavy-duty shock absorbers or the off-road chassis package are required on K-1500 models."
I hope this helps!