I agree that the bigger the truck, the happier you will be. We had an awesome F350 diesel SRW that we used for our 5th wheel - but sold it when we sold the 5er. BIG mistake.
Right now we have a stripped-down Bronco 1200 (probably around 1000#) on a 2014 Ram 1500. We had to add air bags to boost the suspension, because the rear sagged 6" with the camper on it. While the Hemi is doing a good job of getting us up and down the mountains, there still is the general feeling that we don't have enough suspension under the camper, and it's just Ed, myself, and 2 smallish dogs. The quest to find another F-350 diesel will begin once we get home.
Ironically, it will be cheaper to fuel the bigger truck. Ed has been running premium gas in the Hemi to get mid-teens mpg w/camper; but our former 2012 F-350 diesel got 22 mpg by itself (about 13 with the 5er); and I doubt our little popup camper will make much difference to a truck that size.