265/75R16 is the biggest size most tire dealers/installers will put on without having you sign a waiver. Since that is the largest optional size recommended by GM.
The new 285's were a replacement for 265's that were optional equipment when new and the 245 size should be stock on any new 1500 series but you can put a set of 31 12.50s on mine no problem.
Note:
265.75.R16 should fit 2wd, 285.75.R16 should fit a 4X4 although it is possible that one might need to adjust the front torsion bars slightly. The front is the main place you have to worry about fit.