げ details
Examples
with a look of; seeming — a closed set of emotion and sensation words turned into an adjective naming how someone visibly appears
弟、なんか眠たげな顔してるね。
otouto, nanka nemutage na kao shiteru ne.
My little brother's got kind of a sleepy look on his face, huh. casual
彼女は寂しげな表情を浮かべていた。
kanojo wa sabishige na hyoujou o ukabete ita.
She wore a lonely-looking expression. neutral
お客様は少し不満げなご様子でした。
okyakusama wa sukoshi fumange na goyousu deshita.
The customer appeared to be a little dissatisfied. formal
Formation
adjective stem＋げ（寂しげ・不安げ・眠たげ）attaches to adjective (closed set)
Notes
不安, 心配, 忙しい…); a dimension/price word does not join it (×高げ). げ
itself inflects as a na-adjective.
Related patterns
Similar
そう is the spoken default and attaches to almost any adjective for a momentary visual inference read off the scene right now (痛そう "looks like it hurts, from what I can see"); げ skews written/descriptive, is confined to the closed emotion/sensation set, and reads as a lingering air the person carries rather than a snap inference — 寂しげな人 describes someone's demeanor in narration, 寂しそうな人 describes how they strike the speaker just now in conversation.
Lookalikes
Both suffix onto emotion/sensation words, but not the SAME members, and がる is a full VERB reporting observed third-person behavior (悲しがる "acts/shows signs of being sad") while げ is an ADJECTIVE describing how someone visibly looks (悲しげ "sad-looking") — 楽しげ is normal where ?楽しがる is off, and 嫌がる is normal where ×嫌げ is not said.