How did its treatment of conquered people affect Rome's expansion?

The conquering Roman general became the patron of the conquered people, cutting the best deal for them in the Senate. This gave him a large clientele who would back him, and his own soldiers also looked to his patronage also. So Roman aristocrats were anxious the engage in foreign conquests which gave them increasing power. This led to both Julius Caesar's and Pompey's extensive conquests in Spain, Gaul, Britain and the Middle East, and brought them into conflict.

It took realist Augustus to set a limit to the empire behind defensible borders. And a couple of hundred years later emperor Caracalla made all peoples in the Empire citizens to unify them.