Of course,we are just guessing at this point, as the OP hasn't given enough info to gather accurate info.
I looked at the
2002 Chevrolet Silverado sales brochure and on page 10 of 29, right hand panel, it lists detailed info on 2500HD and 3500
fifth wheel towing. Trailer king pin weight for a 2500HD is a max of 3000 lbs not to exceed the vehicle RAWR or the GVWR. Tow capacities for manual and automatic are the same and dependent on cab type, engine type and rear axle ratio.
A 6.0L V8 is a max of 10,00 to 10,500 depending on the cab design and bed length.
A 8.1L V8 is 13,500 to 14,300 again depending on the cab and bed, with a 3.73 rear axle ratio.
The 8.1L with a 4.10 rear axle, the 5th wheel capacities jump to 15,500 up to 16,300 lbs. These are 5th wheel specific numbers, different tow capacities are given for ball hitch trailering. The 3.73 axle requires an automatic transmission and of course the weights given are for base models. Start adding options and capacities drop.
Basically if the OP has a 6.0L engine, he has a problem, if it has the 8.1L, he is good.
Edit: forgot to mention, on both GM/Chev trucks and Dodge/RAM trucks, the rear axle ratio can be found on a sticker located on the inside of the glove box door.
I had a co-worker who sought out and bought a 2005 Surburban 2500 with the 8.1L (in the 'burb they got the 4L80 (or 4L90 cannot remember which) and not the Allison. The 'burb had a 4.10 axle and he towed a car trailer with a mid sized late '60's Plymouth from his folks place in Indiana to Atlanta and said you almost could not feel the trailer behind it.
Charles