Pay Through the Nose.

I.e. Pay heavily. A possible explanation for this lies in the nose tax' levied upon the Irish by the Danes in the ninth century. Those who did not pay had their noses slit.

The Morrises, however, come up with something completely different. In British slang the word rhino means "money". Rhinos is the Greek word for "nose" as we see in rhinoceros.' The Morrises go on to speculate about being bled' of money having to do with nosebleeds.

Source "Dictionary of Word and Phrase Origins", Nigel Rees