About how much does a cup of finely grated Pecorino Romano weigh?

Thank you to whoever said 4 oz per cup. I ground it up in my Thermomix, which worked out perfectly.

I would venture to say 4 oz. It also depends on how compressed it is (and all other factors as pierino put it), but from the flavor perspective 4 oz is a meaningful quantity to use in a dish...

It will also depend a good deal on how you grate it, which will also vary a lot with the hardness of the cheese- a harder cheese will tend to grate somewhat fluffier. I have both a microplane box grater and a regular one- the microplane tends to produce a much airier result. Fortunately, there will usually be a lot of leeway in what will work.

It's a little hard to say because different romano cheeses will weigh a little differently, but about 2 ounces or 50 grams. Some sources say it's 4 ounces or 100 grams. Luckily, most recipes are forgiving when it comes to amounts of cheese.

Here's what Cooks Illustrated says:

https://www.cooksillustrated.com/how_tos/5832-grating-cheese-weight-and-volume