I agree with ETSU - particularly since your ID indicates you are in the Arizona area (and I assume you will be doing most of your hiking in nearby areas where prolonged rain is not an issue.)

A single wall tent would be a great choice - TarpTent makes an excellent product. If price is no object, you might look at the MSR Carbon Reflex series and Big Agnes Fly Creek Platinum series. I only mention them because they give you the option of nearly 100% ventilation by pitching the all-mesh inner without the rainfly. I think TarpTent also has a couple of versions that come very close to this kind of ventilation. I also believe that TarpTent products are slightly roomier than a Big Agnes or MSR product of the same weight. (I know that the Tarptent Rainbow is about 35-50% roomier than the Carbon Reflex 1, but are otherwise quite similar. My own experience, in the Eastern US is that the Rainbow wasn't as well-ventilated - but the eastern US is in no way comparable to the conditions you would encounter. There may be no meaningful difference in ventilation in your part of the country.)

Of course, if bugs aren't an issue where you'll camp, a silnyon tarp (say, 10x12 feet) and groundcloth would be the lightest and perhaps most elegant solution.

The only caution I would give regarding ultralight packing is in regard to the pack. Be careful about going for frameless packs; given that you both have back issues, you may be far more comfortable in a framed pack because it will allow you to carry all the weight on your hips, putting little to no compression or weight on your backs. Keeping weight off your shoulders is harder to do with a frameless pack (not impossible, just requires more care in packing.) Take a look at the Osprey Exos series, or the Osprey Atmos/Aura series (suspension is gender-specific, packbag is virtually identical.) The critical thing is that you can use the load lifers to get all the weight off your shoulders if you want to; that usually means there should be a 30-45 degree angle between the load lifter attachment point on your pack and the attachment point on the shoulder straps. If the clerk at the outfitter store (whether it's the local shop or REI or other big-box) can't help you fit the pack to do this, go look somewhere else.

You don't mention whether or not you and your wife use trekking poles. If you don't, I'd strongly recommend you give them a try; they can really help reduce (but not eliminate) the jarring your back takes when you're on uneven footing (for example, taking a big step off a rock or down from a log.) They are also very handy for pitching that Tarptent or that tarp.

Beyond that, you sound like you've got a pretty good plan on where you go from here, gear-wise. If you've not hiked Grand Canyon before, there are lots of folks who can give you good info on that, too (but I'm not one of them.)

Anyhow, welcome aboard and enjoy your hikes.