To partake in part of the profits of another person's business, usually as a result of extortion. (Used especially in reference to organized crime, particularly "protection money" paid to the Italian Mafia.) Trust me, you're better off just giving him what he wants whenever he comes round to wet his beak. If you don't pay up, you'll have bigger problems.
beak
1. n. a nose. What a beak on that guy!
2. in. to gossip; to chatter. Stop beaking and get to work.