I googled "Moria population estimate" to see if there was some golden thread out there - but I just found this one, as well as a bunch of REAL places called Moria.
Dunno if there's mentioned a headcount of ANY dwarven city anywhere in Tolkien? The we could compare and guess a bit.
Otherwise I suppose the 10 000 estimate which also is pretty random is orthodoxy now - since we are page 1 in google
Another thought in why it might have been easy for the Balrog.
Moria must have had a heavy bueareaycracy + safety measures for two reasons:
Mines always need to control the miners for theft. Seing Moria is mining the priciest of all things to mine, mithril, they must have had extensive rules and laws for who were allowed to mine where, to control if noone was cheating.
Due to them only having few exits, they are very vulnerable to being besieged. It means they must have had huge food supplies + water supplies + heavy safety measures to prevent sabotage.
So I imagine Moria as a place with most people being informed only on a "need to know basis", with a lot of identity paper ("Sir this is a class B mithril mine. We need to know you belong here.") and security clearing etc - a slow inefficient bureaucracy.
Meaning they sucked at adapting their defenses from armies coming from the outside to an unknown enemy from the inside. And their forces were hampered by red tape when they wanted to pass through a mithril mine to blow up the section they thought the balrog was in. etc.