For readily available, non-custom gas blocks...0.936" is as large as they typically go. At that size, you can find a wealth of different options from lo-profile (to fit under most common handguards) to adjustable blocks to...well...you get the idea.
As for how large a barrel diameter...you really do NOT need to go with a 6lb bruiser of a barrel to get optimum accuracy/range/performance from a large-frame AR platform rifle, but to each their own I suppose. As Randall indicated, usually you won't find barrels much larger than 1.050" (give or take a few hundredths of an in.) at their largest diameter. Knowing more about what your end goals are for the rifle would go a long way in helping you find an "ideal" barrel length, contour, twist, etc. Off hand though...Krieger's AR-10/LR-308 "Heavy" barrels are about as big as they come in the industry at nearly 1.1" at their largest diameter behind the journal, 0.937" at the journal, and 0.900" in front of the journal to the muzzle. Similarly, Krieger also offers their M-110 clone barrel which is finished at 20", roughly 0.960" behind the journal (it may be as small as 0.920" but I can't recall off the top of my head), 0.875" at the journal, and 0.850" to the muzzle. Its around 4lbs or so ready to roll which is SUBSTANTIALLY lighter than the "Heavy" barrel (depending on how long you go with the "Heavy"). Again...all academic at this point without knowing more about what you really want/need to reach your desired ends.