Sleep is a habit. During growth spurts, they wake up at off times because they need to eat. After a couple of nights, though, it becomes a habit, and then they continue to wake at that time. Their bodies get use to getting calories then.
Their sleep changes at 12 weeks, by 16 weeks, they start to realize they can get you to come to them, etc. You have to start teaching them to self-sooth, or they will expect you to come whe ever they wake up during the night.
There are threeways to deal with this:(1) let them CIO, (2) go to them and comfort them, but don't nurse!, let them protest cry, but shh/pat them till they go back to sleep, (3) or, you could bring them to bed with you and do the really long road of not getting any real sleep for a very long time.
I did the nurse thing with my first daughter. I didn't get any sleep till she weaned. I have an 8 month old son. He was a great sleeper at the start (8 hours by 5 weeks), but things got really rough around 4 months. I decided to do the shh/pat thing with him, and by 6 months, he was back to 8-9 hours.