quire (of paper), bundle of seaweed, counter for screens, notebook
帖 centers on bound or bundled flat items: a quire of paper, a notebook, or a bundle of seaweed. The counter-for-screens sense extends this idea to flat, screen-like objects counted in units.
帖 combines 巾 (cloth) with 占, which likely contributes the sound. The character originally referred to a piece of cloth or a document, later extending to bound paper and bundles.
A cloth 巾 is used to bind or wrap a stack of paper or seaweed, like a notebook or a bundle. The right side 占 looks like a divination slip tucked into the bundle.
For チョウ, imagine a long-serving chief named Chou carefully counting each quire of paper: Chou -> チョウ, and he keeps the notebooks in order.
folding book
copybook printed from the works of old masters of calligraphy
quire (of paper)
tengujo (thin washi); tengucho
sketchbook
type of commission system in the book industry in Japan
book of calligraphy samples; copybook; portfolio
picture album
Akihagijō (10C poem by Ono Michikaze, regarded as the first hiragana text)
secret notebook
stamp book; pilgrim's passport; souvenir seal album; book for collecting commemorative seals or stamps (at tourist sights, temples, shrines, etc.)