Tweezers were tools used to remove or pick up a small object.
In 2151, Doctor Phlox used tweezers to pick up the litmus paper out of a petri dish and place it on a slide under his microscope for further analysis. He keeps them in a box along with scissors and scalpels. (ENT: "Civilization")
In 2366, William T. Riker opined that there was nothing worthy of salvage on the obliterated Romulan scout ship Pi, unless you used tweezers. (TNG: "The Enemy")
In 2377, Kathryn Janeway used tweezers to remove one of a Borg drone's implants. (VOY: "Imperfection")