Nothing, they hoped Paul would (and if you compare his teachings with the gospels, he was successful) subvert the movement from the anti-organized religion countercultural message of Jesus into something that would either die out or become a tool for them to weaponize.
What would the Romans have hoped to gain by letting someone proselytize that notoriously incompatible-with-the-pantheon religion to the layfolk?
Nothing, they hoped Paul would (and if you compare his teachings with the gospels, he was successful) subvert the movement from the anti-organized religion countercultural message of Jesus into something that would either die out or become a tool for them to weaponize.