depend, rely, evidence, proof, according to, possess, haunt
憑 centers on leaning on something for support or authority: depending on evidence, relying on a source, or acting according to a basis. The possess/haunt sense extends this idea to a spirit leaning on or clinging to a person.
憑 combines 馮 (which historically relates to leaning or depending) with 心 (heart/mind), reinforcing the idea of mental or emotional reliance. The possess/haunt meaning likely developed from the notion of a spirit leaning on or attaching to a person.
The top 馮 suggests leaning or depending, and the bottom 心 is the heart/mind. Picture a person's heart leaning heavily on evidence or being clung to by a haunting spirit.
For ヒョウ, imagine a hyō (雹, hail) storm forcing you to depend on shelter: hyō -> ヒョウ, and you rely on the roof as the hail pounds down.
possession (by a spirit, demon, etc.)
trust; credit; credence
to be possessed
evil spirit (that possesses someone); demon; devil
authenticity; credibility
to possess (someone; of an evil spirit, idea, etc.); to take hold of; to haunt
person possessed by an evil spirit; possession by an evil spirit
to possess; to haunt
child or doll used as a vessel for a spirit invoked by a shaman or miko
basis; foundation; reliance
spirit possession
being possessed (by a spirit); possessed person
cynanthropy
possession by a fox spirit; person possessed by a fox spirit
voucher; documentary evidence of a transaction