paper or cloth pasted together
褙 centers on layers of material bonded together, specifically paper or cloth pasted into a single sheet or backing.
褙 combines 衤 (clothing) with 背 (back), suggesting a cloth backing or lining. The exact historical development is uncertain, but the component relationship is clear.
Clothing 衤 with a back 背 layer: imagine a garment reinforced by pasting an extra layer of cloth or paper onto its back.
For ハイ, picture a tailor saying 'Hi!' as they paste a backing onto the cloth: Hi -> ハイ.