Stakin' in the rain, what a glorious feeling!
We used duffel bags, backpacks and heavy canvas bags.
Stack the lath and bungee cord them together in a small bundle, keep the stack in a contractors bag inside the hub back pull the lath from the center of the stack and write fast.
If it is an option in real trying conditions I like to leave only the offset value on the front and point number on the back and then email the contractor a cut sheet with full info. If the builder is on board with it you can shave some field time that way.
I use an umbrella for rain in some situations, for the operator and note taking, not to protect the instrument, but my situation is not typical.
I use the Panasonic fz-m1 tablet I run my robot with or my water resistant phone to take notes and do the real notes in the truck when finished the job, but I mostly just do residential construction layout (smaller jobs).
I know they say field notes should be done in the field but if they want them to be readable they will be done in the truck.
As far as stakes, I usually only have to do one cut stake for a staking for excavation, so I will put the cut stake in right before shooting it and figuring out the cut and write on it with sharpie as quickly as possible. Or if it's not raining but looks like it will I would do the cut stake first do the ink can dry first.
rain? you work in the rain?