If you have a 2013 Ram 2500 then you should be in pretty good hands. You have more than enough "truck" to handle a FW however the stated weights are low.
In 2013 Ram had not yet introduced the coil rear suspension on 2500 models. In 2013 they did introduce a new higher strength steel frame for the 3500 models and continued to use the old 3500 components for 2013 Ram 2500.
It used to be the only major difference between Ram 2500 and 3500 was one extra spring pack on the rear axle. Back in 2013 when I owned a 13 model year 2500 mine had the Ram 3500 spring packs from the factory. I don't think it was ever officially stated but it appeared that 2013 Ram 2500s were utilizing the remaining frames/suspension components that they could no longer use on the NEW for 2013 Ram 3500 frame.
With all that being said - the decision to go over the stated ratings is your call. It's your family, gear, life etc..
Many will say to NEVER do this and I am mostly in that mindset especially when it comes to halfton models and SUVs but I believe your case is different and should be thought about a bit more critically.
