marry off, pair, match, compare
媲 centers on forming a pair or making a match, often in the context of marriage. The idea extends naturally to comparing two things side by side.
媲 combines 女 (woman) with 比 (compare, match), suggesting the idea of matching or pairing a woman in marriage. The exact historical development is uncertain, but the component relationship is clear.
A woman 女 is compared 比 to find a matching partner. Picture a matchmaker comparing two people side by side to arrange a marriage.
For ヘイ, imagine the matchmaker saying 'Hey!' when she finds the perfect pair: Hey -> ヘイ, and the match is made.