While ago, I read one reason why Christianity grew through the Roman empire was the role of women in the religion. Roman society was male dominated where women did not had much rights and were treated as a property of their husbands or fathers. They were responsible for running the household choirs while men were either busy on front line, administration, and business. Christianity was a religion of the Antiquity where it deliberately targeted women as their converts. This can be traced to missionary work of Jesus (preaching to Samaritan woman, Mary Magdalene, and other women), which was something neither Jews or Greco-Roman society did. Women were surprised when Jesus approached them and carry the idea of early Christianity toward their offspring. Early Christians legends is full of women who were vital for securing foothold of the new religion. Constantine was probably most influenced by his mother Helena and many supporter of the Christianity during the transition period (300-400AD) had Christian mothers while they followed foothold of their pagan father. St. Augustine was another one.
Women are traditionally more religious and dedicated to the faith than men. Christianity utilized on this by targeting them in missionary works. Roman men were not as acceptable to new religion due social and economic structure. They needed to worship an emperor and Roman gods played a role in the administration as a patron of various institutions. Refusing such patronage would lead to end of their political career, especially in the army. Roman military was the last institution of the empire that was Christianized. Julian Apostate was last successful pagan Roman emperor and military leader (+363) where both Germanic and Persian armies were afraid of him. After his death, there was a huge purge of pagan military from the army, culminating during Stilicho (+408) and thus weakening Roman army during Gothic invasion. Rome was sacked two years later for the first time in 800 years.