薄い紙って英語でなんて言うの？

When people are talking about a single paper, they usually use the words "piece of" or "sheet of" before the word "paper."
（「sheet of」とは日本語で「一枚」の「枚」という）
When a piece of paper is not very thick, we refer to it as a "thin" piece of paper--or a "thin" sheet of paper.
e.g.
The present was wrapped in a thin piece of paper.
He always liked painting on thin sheets of paper.

▪ Thin paper
Thin means it has very little thickness.

▪ Slim paper
Slim is another word for thin.

Example sentences:
a. Do you have any thin paper?
b. I enjoy writing on slim/thin paper.

Pencil-thin' means that something is not just thin, but it's exceedingly so. You may use it to talk about paper, or any other materials.

When talking about a unit of paper we usually say a piece or a sheet of paper. Therefore to describe thin paper, we would say :-

1. A thin piece of paper.
2. A thin sheet of paper.

*Thin piece of paper/Thin sheet of paper. - Plural for sheet is sheets. A book is made of sheets of paper.

You can call paper that is thin "Thin paper" or "delicate paper"

Delicate means it can break or tear very easily.

Explanation: The adjective THIN describes something that is narrower than average. If it is very thin, you can use VERY or VERY VERY, or the superlative, the thinnest, or the adverb REMARKABLY.
Example sentence:
'Henry is remarkably good at badmington.'

例：
fine paper (or heavy ) is based on its GSM, (Technical huh?)

GSM is an acronym for 'Grams per Square Meter'.
Quite simply, it allows print buyers and print suppliers to know exactly the quality of
paper being ordered.
The LOWER the GSM number, the LIGHTER the paper
& VIce Versa;-D