lean on, recline on, lie heavy
凭 centers on resting weight against something: leaning on a support, reclining, or pressing down heavily.
凭 combines 任 (which may suggest bearing or entrusting) with 几 (a low table or support), together expressing the idea of leaning or resting weight on something.
The top 任 looks like a person bearing a task, and the bottom 几 is a small table. Imagine someone so tired they lean heavily on the table, reclining against it.
For ヒョウ, picture a heavy person leaning on a table and letting out a big sigh: 'hyou…' The sound of the sigh cues ヒョウ while the weight presses down.