Hug
mid 16th century: probably of Scandinavian origin and related to Norwegian hugga ‘comfort, console’.
wiktionary
From earlier hugge(“to embrace, clasp with the arms”) (1560), probably representing a conflation of huck(“to crouch, huddle down”) and Old Norse hugga(“to comfort, console”), from hugr(“mind, heart, thought”), from Proto-Germanic *hugiz(“mind, thought, sense”), cognate with Icelandic hugga(“to comfort”), Old English hyġe(“thought, mind, heart, disposition, intention, courage, pride”) (whence high (Etymology 2)).
etymonline
hug (v.)
1560s, hugge "to embrace, clasp with the arms," of unknown origin; perhaps from Old Norse hugga "to comfort," from hugr "courage, mood," from Proto-Germanic *hugjan, related to Old English hycgan "to think, consider," Gothic hugs "mind, soul, thought," and the proper name Hugh. Others have noted the similarity in some senses to German hegen "to foster, cherish," originally "to enclose with a hedge." Related: Hugged; hugging.
hug (n.)
1610s, a hold in wrestling, from hug (v.). Meaning "an affectionate embrace" is from 1650s.