To answer A girl and Pete: Michael was not in love with Kay; his marriage to her was not out of love. Thus, he did not care enough for her to abandon his life of crime. He did not care enough for their children to abandon his life of crime. He was not weak; he just plain did not want to give up what he had, really had.

And Pete: his act of betrayal was not abandoning his life of crime or, to paraphrase his own words, the Corleone family will be completely legitimate.