na-adjective, noun
Describes a person, attitude, or expression that feels full of hatred or ill will. Often used for a look or manner that shows dislike.
彼は憎げな目つきで私をにらんだ。
He glared at me with a hateful look.
その言い方はずいぶん憎げだった。
That way of speaking was quite spiteful.
憎い is a more common i-adjective meaning 'hateful' or 'detestable'. 憎げ is a less frequent na-adjective/noun form that often describes an outward appearance or manner.
憎らしい is an i-adjective meaning 'odious' or 'hateful', often with a nuance of provoking irritation. 憎げ is more about the expression of hatred itself.
Formed from 憎 (niku, 'hate') + げ (ge, a suffix indicating appearance or manner). The suffix げ attaches to the stem of adjectives to mean 'seeming' or 'looking'.