The thickness and transparency of the fabric itself is determined by the thickness of the thread and how many threads are woven per inch (thread count).
This is the basics that will determine the weight/hand of the fabric ( in addition to the weave type, but we will be discussing basic weave here).
ex: Article IL020 - Handkerchief Linen:
In this fabric you have a very fine thread (thread size 30 both warp & weft), with a high thread count ( warp 51 & weft 43). This fabric will be translucent, but not see-through; and light in weight/hand.
Ex: Article IL041 - Open Weave Linen:
In this fabric you have thick thread ( thread size 9.09 both warp & weft) and low thread count per inch (warp 20 & weft 19). These properties will make the fabric have a heavier feel/rougher hand, but the fabric will be see-through.