Here are the tow rating for your truck as per the Chrysler web site.
2003 dodge ram 1500 pickup 1500 SLT, REGULAR CAB, 2WD, 6.25 FT Bed, Five-Speed Heavy-Duty Manual Transmission, 4.7L Magnum(R) V8 Engine:
With 3.55 Axle Ratio Axle Ratio You Can Tow 4700 lbs
Gross Vehicle Weight Rating (GVWR) = 6350 lbs
Payload = 1719 lbs
Curb Weight = 4631 lbs
Curb Weight Front/Rear = 2614 lbs/2614 lbs
GAWR Front/Rear = 3650 lbs/3900 lbs
Gross Combination Weight Rating (GCWR) = 9500 lbs
With 3.92 Axle Ratio Axle Ratio You Can Tow 5700 lbs
Gross Vehicle Weight Rating (GVWR) = 6350 lbs
Payload = 1719 lbs
Curb Weight = 4631 lbs
Curb Weight Front/Rear = 2614 lbs/2614 lbs
GAWR Front/Rear = 3650 lbs/3900 lbs
Gross Combination Weight Rating (GCWR) = 10500 lbs
With 3.92 Axle Ratio Axle Ratio You Can Tow 5700 lbs
Gross Vehicle Weight Rating (GVWR) = 6350 lbs
Payload = 1678 lbs
Curb Weight = 4672 lbs
Curb Weight Front/Rear = 2629 lbs/2629 lbs
GAWR Front/Rear = 3650 lbs/3900 lbs
Gross Combination Weight Rating (GCWR) = 10500 lbs
I think you are overloaded now. You can't increase the capacity of the truck without changing the truck.