木 marks 梭 as a wooden object — the weaver's shuttle is a small carved wooden bobbin that flies back and forth through the loom. Same radical in 桌, 椅, 棍 — wooden everyday tools.
夋 supplies the sound, drifting from qūn to suō. You don't see 夋 as a standalone word today, but the same phonetic appears in 俊 jùn (handsome), 峻 jùn (steep), 唆 suō (instigate) — a related sound family.
