I found out, who is laying thin shelled eggs. It is Raggedy Ann.
There were no eggs at 5am. I went out to the coop multiple times, about 30 minutes after coming inside, I went back out, till 9 am. By then all but Blondie laid an egg.
It's windy and rainy at 4:30. I'm going out to open the gate and check for an egg from Blondie.
4/5 today. GC