I bought my F-150 in 2013 and immediately added an extra leaf spring on each side and it made a big difference in the sag and bounce and it didn't negatively affect the ride. That same year I towed our 5200# Roo to the east coast and back on P rated tires with no issues.
Last year the P tires needed to be replaced so I upgraded to Michelin LTs because I knew we would be upgrading our trailer to something heavier and longer than the Roo, which we did this Spring.
The axles and chassis are still the lighter non-HD Payload version which means my GVWR is not changed, but the LT tires and leaf springs do help.
2011 Rockwood Signature Ultra Lite 8293SS, 12K Equal-i-zer
2016 Ford F-250 XLT SuperCrew, 6.2L, 4x4, 6'9" bed, 3.73
2010 Rockwood Roo 23SS (2012 - 2014)
2009 Ford F-150 XLT SuperCrew, 5.4L, 4x4, 5'6" bed (2012 - 2016)