I have leakage out of rear transmission at driveshaft on a 2006 Chevy Silverado automatic, v6 engine over loaded in bed and towing a trailer. Now it slips when engine warms up.

The exact trim level, engine, and powertrain combination of your 2004 Chevy Silverado 1500 Crew Cab Short Box-also known as the 1500 Crew Cab with a 5.8-foot bed-will all play a role in the driveshaft selection. These criteria are usually used to choose the driveshaft for your car, so knowing the right information is crucial if you're wanting to replace or upgrade your driveshaft.
When selecting a driveshaft for your 2004 Chevy Silverado 1500, keep the following factors in mind:
1. **Setup for Drivetrain:** It's possible that your car has four-wheel drive (4WD) or rear-wheel drive (RWD). The driveshaft's design and length will depend on the kind of drivetrain you have.
2.Engine Size: Driveshaft lengths and specs may vary depending on the engine option selected. The torque and power applied to the driveshaft can be influenced by the engine.
3.Transmission Type: The driveshaft requirements may also be affected by the type of transmission-manual or automated.
4.Suspension and Lift Kits: The length and layout of the driveshaft may be impacted if your truck has any suspension or lift kit changes.
5.Options: You have the choice of an OEM (Original Equipment Manufacturer) or an aftermarket driveshaft. While aftermarket alternatives could have different materials or performance characteristics, OEM components are made to match the requirements set forth by the car manufacturer.
It is advised to speak with a reliable auto parts source or a nearby mechanic who can determine the precise specs required for your vehicle to ensure you acquire the right driveshaft for your particular 2004 Chevy Silverado 1500 Crew Cab Short Box. They may offer advice on the proper driveshaft and assist you in locating the part that is appropriate for the setup of your truck.

Which cab design do you have? The two door cab has a 7,050 lb. maximum towing capacity. The four door cab has a 4,400 lb. maximum tow capacity. The information for towing can be hard to understand. Know that the more weight you place inside the bed, the less weight you can place inside the trailer. It is a balancing act and there is a difference between pull weight and load weight. Also keep in mind weight shift and how important it is that the trailer tongue is level (For braking). The front and rear axle weights are on the driver's door jam. Any questions please write back.

Ask for uprated springs or change shocks for adjustable. It could be they are worn and heavy loads are too much for them. Just rear units should sort this.

Towing capacity depends upon trailer design and actual tongue weight of the trailer and load. It also depends upon the condition of your rear suspension, engine size, the condition of your cooling system and if you have an add-on transmission cooler. (for automatics). Last, capacity is also determined by the hitch rating. Generally speaking, you should be able to pull around 5,000 lbs without problems.
If towing long distances or up steep grades it is wise to change the transmission and differential fluid before towing and service those more frequently than normal.

Tow capacity for that vehicle is about 10.000 lbs (adjusted for wear and age). This number reflects max tow capacity with good tires (proper rating and good condition) with all suspension components in good used condition. The capacity of your tow hitch must also match your load and assumes proper trailer weight distribution and tongue weight.
For best results, I also recommend that you use a good quality synthetic gear lube in the differential and synthetic fluid in the transmission, as well as a trans cooler if not so equipped.

With a 20 year old vehicle, the original towing capacity does not apply.
I'd set a limit of whatever the weight of your vehicle is as a safe number (if car weighs 3,200 lbs, tow weight is 3,200lbs Max.) Trailer weight is also determined by the capacity of the hitch.
Trailer loading should be at 60% of weight on hitch.
Don't forget...you need a fully functional cooling system, adequate (most times additional) transmission cooling, and good suspension (air shocks, variable load rear springs and fresh differential lube). If this is done, you may be able to add 20-30% more trailer weight.
One item often overlooked is that it really does not matter if you can pull a load...you need to be able to stop it. Make sure your brakes are in really good condition!!!

rent acar dolly load front of silverado then pull rear driveshaft out an away you go

the 1500 hd rated tow 10300 lb haul in bed 3129lb but the 4x4 tends to reduce tow capacity by about 200 to 400 lbs

As listed in the owners 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. It can also depend
on any special equipment that you have on
your vehicle, and the amount of tongue weight the
vehicle can carry. See “Weight of the Trailer
Tongue” later in this section for more information.
Maximum trailer weight is calculated assuming
only the driver is 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.
The following charts show how much your trailer
can weigh, based upon your vehicle model
and options.
2WD Extended Cab Axle Ratio Maximum Trailer Weight GCWR*
Automatic Transmission,
2.9 L Engine 3.73 3,100 lbs (1 406 kg) 7,000 lbs (3 175 kg)
Manual Transmission,
2.9L Engine 3.73 2,100 lbs (952 kg) 6,000 lbs (2 721 kg)
4WD Crew Cab Axle Ratio Maximum Trailer Weight GCWR*
Automatic Transmission,
3.7L Engine 3.73 4,000 lbs (1 814 kg) 9,000 lbs (4 082 kg)
*The Gross Combination Weight Rating (GCWR) is the total allowable weight of the completely loaded
vehicle and trailer including any passengers, cargo, equipment and conversions. The GCWR for your
vehicle should not be exceeded.

Towing capacity for any vehicle depends on the engine size along with tire size. the towing capacity should be on the ID tag on the driver's side door and will also be in the owner's manual.