My truck does squat when its all hooked up, it actually sits a little lower in the back.
Sorry to be the bearer of more bad news but you have a overloaded 2500 truck. Your loaded drive axle is at 6920 lbs vs a 6500 RAWR/tire/wheel and rear suspension so its not surprising the truck doesn't handle well. Your trucks FAWR and RAWR numbers are on the certification placard on the drivers side door post.
Maximum payload with the 2500HD in stock configuration is 4192
This isn't your particular very heavy 4x4 crew cab diesel 2500 trucks payload. See your yellow tire placard on the door post for your trucks mfg recommended payload.
As Glenn West says your axle/tire rating will determine your trucks actual payload.
Ram may give your truck a 17k tow rating but your particular 2500 truck simply doesn't have enough tire/wheel and rear suspension for carrying your present loads. If you need help understanding Rams Body Builders Guide specs for your particular trucks ratings we can help you with that.
Air bags are needed in your case. If you have 3195 lb 17" wheel and tires you need to upgrade them to 3500-3600 lb 18" tires and wheels.
I know your stressed over the nose high trailer issue and now a overload issue. Many Dodge/Ram 4x4 owners seek help from their truck dealers. At one time shorter rear suspension blocks were a manufactures fix for the rear of a tall 4x4 truck.