What does 경 mean? Is there a root meaning?
경치 - scenery, view
구경하다 - to go sightseeing
Also, is there a meaning for 구 in verb (to go sightseeing) ?
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Sign up to join this community경 comes from the Chinese word 景, which in Modern Standard Mandarin is pronounced jǐng, and in Standard Cantonese ging2. This is also used in Japanese in its on'yomi reading as けい (kei).
On its own, this hanja is given the eumhun 볕 경 gyeong as in "sunshine/sunbeams". However, this meaning has extended to mean "view/sight/scenery" in modern Korean, Japanese, and Chinese, and this extension happened very early on.
구경 is already attested in Middle Korean as 구겨ᇰ〮. It is believed to derive from a hanja-based collocation 求景 = search + view/sight/scenery = sightseeing. This is not used in modern Chinese at all, nor in modern Japanese.