Factory weight ratings
From the 99 sales brochure page 24 and 25; 3500, 2wd, automatic transmission, 3. 54 rear axle ratio: GVWR is 10,500 lbs, GCWR is 16,000 lbs, max trailer weight is 10,000 lbs (note 5) . Note 5 states that any trailer over 10,000 lbs requires the use of a 5th wheel hitch. If you had the 4. 10 rear axle ratio it would be rated with a GCWR of 18,000 lbs. (All other weight ratings remain the same).
Now the hard part my 97 2500 weighs 7400 lbs empty with me in it and full of fuel. I would bet that your 3500 weighs more than my 2500. If we estimate that your truck weighs 300 lbs more, then I would estimate that your truck weighs 7700 lbs (conservative estimate). Therefore: 16,000-7,700 = 8,300 lbs for your max trailer weight. If you had the 4. 10 then it would be 18,000-7,700 = 10,300 max trailer weight. Note that with a manual transmission and either rear axle ratio the GVWR is 20,000. 20,000 -7,700 = 12,300 max trailer weight. If you are interested in a lengthy discussion on this topic see "3/4 tons must be great" in the towing and hauling forum. Hope this helps. Ken Irwin