Well, in its day, Rome was not 3,000 years old, so if your city managed to survive and thrive over all that time, and is still prospering after all that time, then it would probably be a lot bigger. The Rome of today supports a population of maybe 2.5 million people. The original village was founded at around 800 BC, so you could say that the city is now reaching towards that 3,000-year mark.
Anyway, Rome's prosperity was achieved because of a lot of good luck and chance events in the favor of the city -- she was *really* lucky to wind up with the status she would eventually see. So if you rewound time and let the course of the world happen again, you probably wouldn't get the Rome we have today.
I don't know if this helps any. Is there something more specific that might be of use?
Oh! One or two more things.
Rome's population was surprisingly small for two reasons.
First, because of their aggressive nature, they were constantly expanding, conquering and expanding again, and the death toll from the constant warfare, combined with the fact that they'd seed newly-conquered territory with Roman citizens, resulted in a much smaller population of citizens who actually lived within the boundaries of the city proper. Furthermore, second- and third-born (and so on..) sons who had no claim to their father's estate could volunteer for military service and would then be stationed all over the empire.
Secondly, in a deliberate move to control the city's permanent population, citizens could volunteer for Rome's near-constant stream of colonization projects, where they would be given land and would be allowed to make a name and a living for themselves by founding an outpost city hundreds of miles away from the main body of Rome.