Word for very-fine, see through

Solution 1:

Diaphanous, from Greek diaphanês "transparent, translucent", from dia "through" and phainô "to shine, appear".

Solution 2:

A synonym is sheer(^2), adj. [< ON. skaerr, bright] 1. very thin; transparent: said of textiles (Webster's New World Dictionary, Warner Books Paperback Edition, c. 1984), in case you need variety from lovely "diaphanous."