Unsecure chicken perches

[njoy]

My little Lottie often has one eye closed. She is about 16 weeks and has done this on and off since I had her, it seemed to be just when she was resting and the one eye would close first, but now she seems to do it alot. My other pekin used to peck her but this has stopped now. I was wondering is this just a quirky thing, there seems to nothing wrong with the eye, it is bright and clear when open, or a sign of something else. I had also been thinking of getting a couple more pekins, but am now worried that she will be picked on by new hens.