Are counterweights used on the booms of sailing ships?
No there is no counterweight. When the sail is furled the boom is held up by a line (called the topping lift) from the far end of the boom to the top of the mast (and then through the mast to the foot so that it can be controlled). When the sailed is hoisted the boom is held up by the sail (or rather the sail is held down by the boom). Fairly modern sailing yachts can have in-mast furling mainsails (my yacht does). This means that the sail is furled by being rolled around a vertical wire stay inside the mast. In this system there is a small block called a traveller (which might look like a ball on some boats) that slides along the boom as the sail is unfurled. The line that pulls the sail out (called the outhaul) runs through a turning block attached to this traveller (that might look like a ball too). It’s purpose is to keep the back edge of the sail (the leech) taught during furling and unfurling to prevent the sail jamming in the small slot in the mast through which it runs.
