I have only been there once, so don't have any particular expertise or insight. But it is was in May, right around when you are going. We were surprised that it was full on winter conditions on the rim, below freezing, snowing heavily, and windy. The trail was snow and ice covered for the first few hundred feet. Looking back on the expected weather for the rim in May, I don't think that was all that unusual. We camped up high, maybe 2/3 of the way back up, on the last night, and it was very cold there that night in the wind. It was essentially summer at the bottom, and the temps warmed up rapidly as we dropped in.
But a hat and light gloves would be worth considering, even bringing to the rim just in case. If you are camping anywhere above the bottom, I would also think about a light layer for under the pants.
We cached food and water for the last night, so we didn't have to carry that. I used just a lightest plastic food storage container from the grocery store. I am sure a rodent could have chewed in; but it was mostly odor proof and plastic containers are used all the time to deter mice. So that would be the almost free option for food.
I hung our food off a small ledge at camp down at the bottom. Probably not a good idea, but was the best I could come up with. That was actually attacked by crows, but we happened to come back just then.
enjoy the trip.