Final answer:
Haemon is the character who tears up at the sight of Antigone being led into the room, due to his deep love for her and their impending marriage.
Step-by-step explanation:
The character who starts to tear up at the sight of Antigone being led into the room during Sophocles' play Antigone is Haemon, who is betrothed to Antigone and is the son of Creon. Haemon is deeply affected by the fate of Antigone and later pleads for her life, threatening to die with her if she is not spared. The relationship between Haemon and Antigone is a pivotal element of the tragedy, highlighting the personal conflicts and the tragic consequences of the characters' actions.