Growth spurt (not sleeping)

My LO is 7 weeks and is definately going through a growth spurt. He has eaten every hour since 9pm tonight. He had 5oz at 9 and 2oz an hour since then. But he seems like he is tired but won't go to sleep. He closes his eyes for a minute or two and then wakes back up or he falls asleep for maybe a half an hour. I'm just wondering if it's ok for him to be up like that or if he should be sleeping more because of the growth spurt? Thank you guys :)