〜げ
-looking, with an air of
い-adj stem · な-adj stem · たい stem + げ (な / に / だ)
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げ describes how someone appears to feel, judging from their face or manner: 彼女は悲しげな顔をしていた, "she had a sad look on her face".
It attaches to the stem of an adjective (悲しい → 悲しげ, 楽しい → 楽しげ, 寂しい → 寂しげ) or to たい (言いたげ, "looking as if they want to say something"). It works like a な-adjective: 悲しげな顔, 楽しげに遊ぶ.
It's close to そう (N4, "looks like"), but more literary and more focused on emotion and atmosphere. You'll meet it often in novels.
A few set phrases use it too: 自信ありげ, "with an air of confidence"; 意味ありげ, "meaningfully".
Examples
彼女は悲しげな顔をしていた。
She had a sad look on her face.
子どもたちは楽しげに遊んでいる。
The children are playing happily.
彼は何か言いたげだった。
He looked as if he wanted to say something.
自信ありげに答えた。
They answered with an air of confidence.
寂しげな後ろ姿を見送った。
I watched them walk away, looking lonely.