Well, yes, leaders have often instituted a state religion change in order to shore up their power. I don't think it was because Christianity was inherently weak.

Christianity survived despite sometime Roman efforts to eradicate it. I'd say Christianity was, if not strong, then at least persistent. I think Constantine saw the value in a religion that was evangelical. That welcomed new adherents and that people could mass-convert to. It probably seemed new and interesting coming from the frontiers of the Empire.