There is a quote from Tolkien that touches upon the question of the Fellowship's recognition of the Balrog.
Quote:
[The Balrogs] were supposed to have been all destroyed in the overthrow of Thangorodrim, [Morgoth's] fortress in the north. But here it is found (there is usually a hang-over especially of evil from one age to another) that one had escaped and taken refuge under the mountains of Hithaeglin (the Misty Mountains). It is observable that only the Elf knows what the thing is-and doubtless Gandalf.
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Letters # 144
Being an unrepentant pedant, I note that Tolkien says not that
Legolas knew the Balrog, but "the Elf" did so. To me that supports what I (and others) said: that it was not Legolas as an individual that gave him any special insight, but his race. Note that Tolkien also says that Gandalf did indeed know it for what it was. Perhaps his "now I understand" remark could mean that he then fully understood what
Durin's Bane was, and how it had affected the Dwarves in Moria.