i remember a lot of folks buying BIG 5w trailers on this forum at the time towing with a 2500HD. A year later trading them in on a dw rig. Towed fine, bottomed out the RA a lot.
limit on rear is due to the tires. reality tge springs are good to 6400. BUT, dump a 3-4000 lb pin load, you're in trouble. My 96 CC LB 6.5 with similar specs, was closer to 2200-2400 empty on the rear. My swag is the 02 will be around here, about 4400-4600 on the FA.
IF you pack heavy, you may overload this truck. if an occasional move, it will do the job legally if you have enough tonnage on it. A ball mount trailer you can pull about double the wieght of a 5w for a given chassis truck, dur to less hitch wieght. you may want to go to a longer TT.
GCWR on my 05 dmax was 21000 for a SW rig, 23500 for a DW rig. I believe the 02 was the same.
marty
92 Navistar dump truck, 7.3L 7 sp, 4.33 gears with a Detroit no spin
2014 Chevy 1500 Dual cab 4x4
92 Red-e-haul 12K equipment trailer