16 day old eating 2 oz every hour right now!

Brit
Is this normal or safe? He is acting so hungry so I give him an oz of pumped milk. A few minutes goes by and he wants more so I give him another oz. so far he has had 2 oz every hour for the past 2 hours. Am I over feeding him? 
It's not just crying that makes me think he's hungry still. He is actually giving hunger queues such as sucking on hands, arms, and looking around for a nipple with his mouth open. 

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