What causes deviled eggs to 'weep'? I've made deviled eggs hundreds of times over the years. On rare occasion, after being refrigerated, they weep.

I always follow the same procedure, making sure that the egg whites are completely dry inside and out. I let my diced pickles drain thoroughly. Basically I take every step to ensure that there is no unnecessary liquid. 

99 times out of 100, they don't weep. But there's that one time that they do. I made some yesterday, and today there was an unreal amount of water in the covered dish. (They've been refrigerated since immediately after I made them.)

I should mention that all ingredients were cool to cold. Everything but the eggs and salt came from the refrigerator, and the eggs were quite cool from being immersed in ice water after boiling. 

Putting everything together is a pretty quick process, so they didn't sit out for any extended period of time.

As I always follow the same procedure, what factors could cause them to weep one out of a hundred times? Could humidity be a factor? (Wondering about that as the humidity in my area has been extremely high the last few days, ~85% inside.)
Assuming it isn't condensation, one thing that causes eggs to weep is the breakdown of the protein structures. 

When you cook an egg, the heat causes the proteins to unfold, then refold into different shapes, capturing liquid in the process which is what allows the boiled egg to hold it's structure. These bonds are fairly weak and can be broken down with salt and acids--two things which you have in your deviled eggs. 

One thing that might help is slowing down the unfolding/refolding process by putting the eggs in before the water is fully heated and not heating the water up to a full boil. By slowing down the process you are building stronger bonds that won't break as easily. You might also want to experiment with the cooking times, it could be that those times you encountered weeping they weren't cooked long enough to build strong bonds.