You will likely be over your listed payload, which is probably around 2300 lbs. That being said, you will be way under your rear axle rating. Your truck will handle the weight just fine if you chose to pull this trailer.
t you have to keep in mind over your weight limits is illegal reguardless wether you add bags or not. My .02 a 2500 with bags is no different than a 3500 srw other than the legal side of it.
What makes it "illegal"? There are two things that make you "legal" when it comes to weight.
The most important is federal bridge weights, which I believe are 20,000 lbs per axle. I don't think the OP will exceed those ratings, and even if he tried I don't think his truck would be able to move that weight. Under the federal bridge weight limits, perfectly legal on that point.
The second thing is your registered weight. You can legally haul any weight you want, so long as you are registered to carry that weight. In Maryland, vehicle weight classes are 7000 lbs or 10,000 lbs (amongst others...). I had a 2010 Tundra that was rated by the manufacturer of 7200 lbs. I could either register for 7000 lbs and "lose" 200 lbs of payload, or register for 10,000 lbs and "gain" 2800 lbs of payload. So long as the OP pays to register his truck for the amount of weight he is carrying, perfectly legal on that point.
The number assigned to the truck by the manufacturer is arbitrary. They are a compromise between marketing, engineering and legal departments. They are not legally binding in any way, shape or form.