Just to add two bits worth here ... one of Constantine's major achievements was to stabilize the currency which had been in runaway inflation mode up to this point. (The new coinage of the libra, solidus and denarius made up the £.S.d which anyone familiar with British currency until a few decades ago will recall.) This stabilization was done by using temple treasure, and in the process peeving quite a few devout pagans.
Therefore C. needed political support to balance those alienated pagans. This support was most easily obtained from those who had no interest in keeping treasure in the temples - i.e. the Christians. Not saying this was Constantine's only reason for backing the Christians, but given his general cynicism, I'd say it was certainly on the list. (Have you noted the total lack of Christian iconography on his triumphal arch, which was built somewhat earlier?)