Beauty is but skin deep (6)

I believe the answer is:

veneer

I'm a little stuck... Click here to teach me more about this clue!

'skin deep' is the definition.
'veneer' can be an answer for 'skin' (thesaurus). I am unsure of the 'deep' bit.

I can't explain the remainder of the clue.

Can you help me to learn more?

(Other definitions for veneer that I've seen before include "A surface coating or skin" , "A thin layer on the surface, often wood" , "Mask; gloss" , "Thin wooden facing" , "Finish" .)

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