The number of Balrogs has changed in Tolkien's mind. In the beginning there were thousands of them, and they were quite weak. For instance, when Fëanor is surrounded by Balrogs, Tolkien thought of them as far weaker and numerous than in later writings, such as The Lord of the Rings.
Morgoth flees from Valinor with the Silmarils, the magic gems of Fëanor, and returns into the Northern World and, rebuilds his fortress of Angband beneath the Black Mountain, Thangorodrim. He devises the Balrogs and the Orcs. The Silmarils are set in Morgoth's iron crown
It is notable that the Balrogs were still at this time, when The Lord of the Rings had been completed, conceived to have existed in very large numbers (Melkor sent forth 'a host of Balrogs');
Those are quotes from The History of Middle-Earth (HoME).
In the end, he decided that there were seven of them.
In the last version, the balrogs are Maiar who were attracted by Morgoth's power and corrupted by him. So they do not reproduce (only Melian among the Maiar did), nor were they created by Morgoth.
Orcs are beasts and Balrogs corrupted Maiar.
Note that we only know the number of Balrogs through Christopher Tolkien, who compiled his father's writing. However it's quite obvious when reading The Silmarillion that they grow stronger. In some earlier versions there are entire armies of Balrogs, which would be ridiculous – were they as powerful as shown in The Lord of the Rings.
All that info comes from HoME, which is not completely canonical, as it's not approved for publication by Tolkien.
Edit1: see Lost Tales, Part II, "The Fall of Gondolin"
Edit2: There is some commentary in the Lost Tales about the number of Balrogs, but nothing about the number seven. If anyone knows where the exact quote is, please edit this answer.
Edit3: I have it!
'a host of Balrogs, the last of his servants that remained' ) 'his Balrogs, the last of his servants that remained faithful to him'. In the margin my father wrote: 'There should not he supposed more than say 3 or at most 7 ever existed.'
From HoME. It's written by Tolkien but never published.