lean on, post, prod, ridicule
拄 centers on using a stick-like object to support or prod: leaning on a post, poking something, or figuratively prodding with ridicule.
拄 combines 扌 (hand) with 主, which likely contributes the sound. The exact historical development is uncertain, but the character is associated with actions done with a hand-held stick or post.
The hand radical 扌 holds a 主 (master) stick, like a walking stick you lean on or a prod you use to poke and ridicule.
For チュ, imagine leaning on a post and chewing gum while you prod someone with ridicule: chew -> チュ.