Do you remember what the emmisary of Sauron said to Dain, King of the Lonely Mountain:
Quote:
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Find it (The One Ring), and three rings that the Dwarf-sires possesed of old shall be returned to you, and the realm of Moria shall be yours forever. (II, The Council of Elrond)
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This suggests that if Sauron knew of the Balrog in Moria, he was also in control of him.