These are the numbers from my '13 350 CC 2WD for reference:
Front / Rear GAWR. 5000/6730
Front / Rear weight. 4580/3360
These numbers are for our truck loaded to travel and includes the hitch. Your weights will differ based on trim, options, drive train, passengers, and "stuff" you're carrying. In my case it "suggests" that my max trailer weight would be around 13,480#.
The CAT Scale is your friend.
2013 F-350 CC SB 2WD 6.7PS
2013 Eagle Premier 351 RLTS
-SOLD- 2012 X23B
-SOLD- 2003 Ford Expedition 5.4, Bilstein shocks