I just got back from the Grand Canyon too. Hiked the first week of May.
I wore some fairly heavy long pants (some type of nylon that breathes and acts cotton...actually not that heavy), and a t-shirt. I wore military liner socks with military oversocks (at least Canadian Military). Heavy leather boots. An Outdoor Research Sun Hat.
The sun was intense, but there was occasional breeze. Absolutely no shade and the ground has a tendency to bounce the sunlight all back up at you.
I found my sunscreen stopped working (sun too intense or maybe sunscreen expired, it was UPF 60). My arms were starting to burn by the end of the first day. As the forecast was for brighter, warmer weather, was getting worried. So, I took a pair of the long linger socks (black, thin, synthetic), cut the tips off them and wore them as arm coverings. I anticipated that they would be ovens, but protect my skin. In the end, I discovered a new clothing item that will come with me at all times. Not only did it protect my skin from the sun, it distributed and retained my sweat long enough to control how it evapourated for maximal benefit. My arms, covered in black socks became the coolest part of my body. They were downright chilly at times. Further, I could dump some non-purified water on the socks, and they would stay wet and slowly dry over the length of about 30-60 minutes (combined with sweat additions) to keep my arms chilly in the 90 degree heat.
As for the pants: the different between pants and shorts is the difference between being afraid and cautious (slow walking near) of cactus or being appreciative of cactus beauty without needing to slow down to gingerly avoid it.
After that, I carried a bunch of clothes that I just did not use. Well, not true. I used the two pairs of underwear I brought as extra and did make use of my extra full set of socks. And, I used my low-profile rainjacket and toque for warmth and bug protection at night.
Oh, and I made use of some biking gloves, which saved my skin and nails from sunburn (sunburn on the nails is torture)
My extra shirt, down vest, long sleeve undershirt, shorts, long johns were absolutely unused (hey don't laugh at me, I am from Canada, where it is bred into the genes that every hiking trip will have snow).