Why did the Greek city state never form an empire?

The circus in Arles

Ortigia, the heart of Syracuse.

A restored Roman domus in Aix-en-Provence.

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The Greek theater in Syracuse

Massilia in the ancient times.

Vestiges of the Greek city of Oblia (Hyeres) which isn’t very far from Marseille.

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The temple of the imperial family in Nimes.

They did. Athens or Syracuse were the heads of confederation of cities. But the Greeks never had a heavy interest in territorial domination, what structured their action were business network. This was clearly illustrated by the history of Massiglia. The Greeks acquired lands in what is now Marseille, and a few places where their farms mixed with local farmers. The cities were just places in which authorized citizens made decisions and worshiped the gods. They mostly traded goods and artifacts, some of which were very expensive. For controlling the navigation on the Rhone river, they only set a few military positions at the critical points. When the Romans allied with Marseille, the traded items become in the major part slaves whose travel couldn’t be differed because the traffickers had to feed them. So the Romans created three colonies Aquea Sextia (Aix-en-Provence), Arelate (Arles) and Nimosis (Nime) where they settled military retired veterans to secure the area.