[Lord Melkor]

Hmmm, interesting topic. I think Rumil made some good suggestions about that first year of the Balrog's release. I reckon the Balrog first killed the Dwarves that awoke him and lingered for a while in the deep places of Khazad-dum to regain his bearings. After all, he was asleep for thousands of years before being rudely awakened. I think some of the miners escaped back to the upper levels and warned their lord, Durin, who decided to venture down there himself with a strong detachment of Dwarven warriors to teach this creature a lesson in Dwarven hospitality. Unfortunately he got a lot more than he bargained for and was duly killed by the Balrog, who must have been getting pretty annoyed by all these Dwarves prancing around him.

For the next year the Dwarves would have probably tried to contain the Balrog in the lower levels by sealing the corridors and hallways leading there. Obviously their efforts were in vain when at the end of that year the Balrog broke out and killed Nain. Now that the Balrog had broken through to the main halls of Khazad-dum and having lost two kings and probably a good deal of their best warriors, the Dwarves were compelled to hastily evacuate Khazad-dum.

It seems probable that the Balrog and Sauron (who resided close-by in Dol Guldur) had some sort of 'gentlemen's agreement', where the Balrog would allow Sauron's orcs to inhabit Khazad-dum, as long as they acknowledged the Balrog's supremacy in Moria. Though not stated outright in the books it seems the Balrog resided mostly in the lowest levels of Khazad-dum, close to his original resting place. I believe Gandalf remarked that though the upper levels had been completely plundered, no-one dared to venture into the deeper levels, stating that these are clouded in the shadow of fear (aka, the Big Bad Balrog resided there).

This would also explain why the Balrog allowed Balin's expedition to continue for so many years. It may be that the Balrog was simply unaware of them, with the dwarves only inhabiting the upper levels of Khazad-dum while the Balrog resided in the deep, lower levels. Only after the Orcs returned into Moria was the Balrog's ire aroused, though it may be that the Balrog himself never actually attacked Balin's dwarves, instead preferring to let the Orcs do the cleaning out.