Cyrodiil is a wealthy province, despite its desolation. If Cyrodiil spent its day svcking money from Skyrim, we would know it. Not even Stormcloaks say anything about Skyrim's assets being directed to Cyrodiil. If anything we hear of Cyrodiil sending large amounts of money to Skyrim to make sure its Jarls stay loyal, and as far as I know the Jarls generally use those funds to the well-being of their people.