The Tweigar, a freighter, was owned and operated by Captain Gormo in the time leading up to the Onderon Civil War.
While on a business trip to Onderon, the Tweigar made planetfall in Iziz, but while Gormo was visiting the city his starport visa was pilfered. Because he was stranded in Iziz without the necessary visa, Gormo was unable to return offworld or even get back to his ship, which was located at the starport. Despite the Tweigar's crew coming to the checkpoint and confirming that Gormo was indeed their captain, the Onderonian soldiers were unmoved and refused to let Gormo pass. Gormo was infuriated by the Onderonian soldiers' rigid adherence to protocol, which stated that no one could enter the starport without the proper visa. He told Meetra Surik that if he ever managed to leave Onderon, he would never return.
The ultimate fate of the Tweigar is, in part, determined by Meetra Surik's choices. Surik can give one of the two available starport visas to Gormo. If Surik gives Gormo a visa, he immediately goes back to the starport, reunites with his crew aboard the Tweigar, and they leave Onderon. If Surik does not give Gormo a visa, the Tweigar's crew was either stuck on the planet waiting for Gormo when the Onderon Civil War began, or they were forced to depart without him.
Gormo does mention the possibility of his crew leaving without him, explaining that due to the high likelihood of a civil war breaking out on Onderon, and the fact that his ship was operating on a strict timetable, his crew would be unable to wait for him indefinitely.
The Tweigar is only ever mentioned by its captain in conversation with Meetra Surik, it is never actually seen in the game.