The yellow sticker weight of my White Hawk is 432# more than the published unloaded vehicle weight. Fully loaded CAT scale weight 5960 trailer axle and 720 hitch. This includes 1/3 tank of fresh water. (about 100#) This is about 1000# more than my old 26BH. This is 1280 lbs above the listed unloaded vehicle weight. If you load your trailer in a similiar way you wil have around 6600 total with 700 on the hitch.
I would think your truck should be ok with this and I would not make any mods until I tried it out.
2012 Toyota Tundra 5.7 Litre DoubleCab
6 speed, 4.30 Limited Slip, Tow Package
2013 Jayco White Hawk 27DSRL
2010 Jayco JayFlight 26BH sold
Yamaha EF2000is Generators (2)
1996 Honda CB750 Nighthawk