My opinions based on several years of noting fuel mileage and tire size differences and running a "few miles" offroad:
-wheel material doesnt seem to make any noticeable difference in weight or fuel mileage. The design has far more effect on this. Bling-bling thick aluminum chromed dubs are lead weights compared to a good set of inexpensive common steel wheels.
-wheel DIAMETER can have a very dramatic difference. Larger wheels are heavier and the weight is carried further from the axle centerline. This will hurt your fuel mileage. Switching from 15" to 20" wheels can drop mileage by over 20 percent, even if overall tire diameter remains the same.
-MT's vs AT's: MT's are most often heavier than AT's due to the deeper tread. Once again, more weight further from the axle centerline will hurt mileage. For a DD, AT's will do much better for you.
-hate to disagree, but there is no way wheel width will ever pinch a sidewall and increase tire diameter. Running too narrow of a wheel may angle the outer tread down toward axle centerline and make the contact patch screwey, but never make a tire "taller". I will say that running a standard 33/12.50-15 on a 15x8 wheel works very well, especially for keeping the bead seated when running very low pressures offroad. 15x10's with the same tire loose the bead WAY easier.
-most companies post tire weights, or you can find them online. Lighter tires will have a ton of advantages over heavier ones. Unless you are running rocks and need a ultra-thick sidewall, go as light as you can.
-the Interco Iroks wear fast and are not a great DD tire, but they are some of the best performing and lightest offroad tires out there. They are also available in 31" and 33" sizes as the Irok ND (non-directional).
-for offroading, I prefer to buy a tire with Road hazard Warranty. I am running Firestone Destination MT's (33x12.50x15). They are a really great all-around tire with great treadwear performance.
-with 4:88 gears, I think you are better off with 33's than 31's.