Technically we already do, but indirectly.

In order to get a 250g rock up high enough to reach it's terminal velocity before hitting the earth again, you'd need some kind of launcher (e.g. catapult, trebuchet, Slingshot, etc) which are regulated. For example, New York made Slingshot a Class-4 misdemeanor.

I'm pretty sure that regularly throwing half-pound rocks high in the air is already regulated.

Perhaps in some urban areas, but I seriously doubt there are federal regulations about throwing rock projectiles into the air with no intent to hit or harm a person.

FAA says that pilots may drop objects from airplanes, but puts the onus on the pilot to ensure "no hazard is created". And, once the object touches the ground, it becomes subject to local laws. So dropping a rock onto someone's property could be quite a few violations depending on the outcome and the property.

The question was concerning throwing rocks "up into the air", not throwing projectiles from an airplane.

If it involves airplanes, you can rest assured that the FAA will regulate it, so no surprise there.

I don't imagine there are terribly many rocks getting 100m in the air except by human action.

Only if you're flying rocks at over 328 feet in the air.