According to the story(there actually is a Entering-Gensokyo story about it), Remilia is not equipping Gilgamesh, she's merged herself with Rebellion.
Rebellion's true name is Rebellion Scarlet, mother of Remilia and Frandre. She fought alongside Sparda 2000 years ago against Mundus. After the war, she challenged Sparda to a duel, lost and turned herself willingly to the sword Rebellion.
According to the story(there actually is a Entering-Gensokyo story about it), Remilia is not equipping Gilgamesh, she's merged herself with Rebellion.
Rebellion's true name is Rebellion Scarlet, mother of Remilia and Frandre. She fought alongside Sparda 2000 years ago against Mundus. After the war, she challenged Sparda to a duel, lost and turned herself willingly to the sword Rebellion.