Back to history class, WF. The state religion of the Roman Empire was NEVER Roman Catholicism. As a matter of fact, the Empire tended towards accepting a "broad diversity" of beliefs which included heresies. It did this for pretty much the same reason which underlay the Elizabethan Compromise, to keep the peace. You should also know that The Church, in Alexandria, Antioch, Constantinople, Jerusalem and Rome often found themselves in opposition to heretical Emperors, to the point of anthemizing those Emperors and/or loosing their patriarchates or even their heads over those oppositions. Whole Councils of The Church came out in opposition to various Emperors and won.
Let's take a jaunt down memory lane. ;-)
While I think you can make the case that Roman Catholicism became the de facto state religion with Constantine opening the council of Nicea, (determining who could attend and paying to have them there) the moment I believe that Roman Catholicism became the state religion was when Ambrose excommunicated Theodosius for conducting reprisals against the citizens of Thessalonica, who had murdered a barbarian army commander. Theodosius was only readmitted after doing public pennance. It was after this that the legal code began to be used to eliminate the role of the pagans.
Ambrose is an interesting study because so much happened during the time he was Bishop of Milan (373-97). He came from the ruling class and was transformed from being a layman, not baptized, into a bishop within 8 days. He is also the bishop that baptized Augustine