If the moon smiled, she would resemble you.
You leave the same impression
Of something beautiful, but annihilating.
Both of you are great light borrowers.
Her O-mouth grieves at the world; yours is unaffected,
And your first gift is making stone out of everything.
I wake to a mausoleum; you are here,
Ticking your fingers on the marble table, looking for cigarettes,
Spiteful as a woman, but not so nervous,
The moon and the rival both turn everything grey and immovable: the moon literally, in that bright moonlight, turns the world grey as stone, and figuratively, through her domination and judgement, makes a body afraid to move as any action will displease her. 
 The rival, on the other hand, petrifies a situation into careful and trope-tastic roles: Wife, Rival, Husband/Object. No one can move under either gaze, or at least, not in this situation. 
 In further contrast, the moon is turning the world to stone out of pity, grieving for the world’s pain. However, The Rival is ‘unaffected’ by the world’s pain and it can therefore be presumed is turning the world/a room/ Plath herself to stone maliciously. 
 The line may also be an allusion to Medusa, a monster in Greek mythology who was so dreadful she would turn all who looked at her to stone. Indeed, Plath wrote a poem called  Medusa  for the same collection, which explores her relationship with her mother. In this poem, her mother is portrayed as overbearing and suffocating.
The Rival