Will I be permitted to pack a cheese grater in my carry-on bag for a domestic U.S. flight, or will this be considered a "potential weapon" and prohibited?
It probably depends on how your cheese grater is constructed. You can see the official list of prohibited items on the TSA web site. The most relevant section seems to be the "sharp objects" section, which lists:
However, others likely would be considered 'sharp objects'.
It also almost certainly depends on the judgement and mood of the person on duty who checks your bag.
I was once forbidden to take marshmallow cream in my carry-on, because it was "liquid." (Try pouring marshmallow cream, and then tell me its a liquid!)
According to the TSA's "Can I Bring..." web site (also available on their Mobile App) you CAN bring your Cheese Grater in either Carry-on or checked-in luggage.
This is potentially one of those situations where it would be worth carrying a print-out of that page showing that it's OK, just in case the TSA agents decided that it was not allowed.