I was talking about City Prestige, sorry for the confusion. Getting +5 to City Prestige from a building with high labor costs and a tier 2 tech requirement would allow one city to rocket past expansionist nations. Building it would not be ideal for an expansionist, who needs to build lots of units. Call it Refuge District and either make it a dead end tech or add it to Administration. Of course it would be nice to have Tower of Dominion and Beacon of Hope add +3 Prestige to a capital.
That way:
A one city strategy would get [(5 FactionPrestige)+(5 From RefugeDistrict)+(3 Tower of Dominion)+(.5 Inn)= 13.5] prestige in the capital in about 50 turns.
A two city strategy would get [(5 FactionPrestige)*(.5 HavingTwoCities)+(3 Tower of Dominion)+(.5 Inn)= 6] prestige in capital in about 50 turns. The minor city would have 3.
A three city strategy would get [(5 FactionPrestige)*(.33 HavingThreeCities)+(3 Tower of Dominion)+(.5 Inn)= 5.17] prestige in capital in about 50 turns. The minor city would have 2.17.
The prestige advantage goes to the small nation, while the larger ones have the ability to train many units. The small nation has fewer upkeep costs per population and can afford more of them due to the high population. This also means more research and thus better technology. From just one Study you would get +20% research to all your research power at only one maintenance.
That is how i would balance it.