I suggest sticking to a 3 hour schedule (that's all day and night) and in the middle of the night you do have to nurse and wake the baby up after 3-4 hours to ensure proper nourishment until his 4th week when you allow him to wake up during the middle of the night on his own (trust me, he will). Your baby needs to be on a schedule b/c this will help regulate his metabolism, which will help him sleep through the night when his body is ready. Right now, he can't distinguish between day and night. He's got his days and nights mixed up. That's normal for all newborn babies. With a schedule, it will help his body get used to sleeping more at night and being awake more during the day.
At 2.5 weeks old, a 3 hour feeding schedule would work as long as the feedings aren't snacks, so nursing and burping can take up to an hour long. Anything longer than 1.5 hours of being up would be too much and he will end up crying for a long time due to over-stimulation or fall asleep then wake up crying. Not much "wake time" is needed after a feeding at this age. And you need to keep the baby awake and not let the baby dose off while nursing or he will be snacking and will wake up usually 40-60 mins after for more. Try taking off his socks or just having a onesie on with a thin receiving blanket. Being too warm with a half full tummy will make him dose off even though he wasn't quite finished.
Night feedings are quiet and relatively dark. We used a flashlight. No TV, music or talking during this feeding. Try to do this feeding as quickly as possible.
We had both our daughters on the babywise method. Controversy or not, it works. And babies are able to sleep long periods after 8 weeks (6-7 hours). As your baby grows, the hours at night increase, while the number of feedings decrease and the baby will take in more food at each feeding.
Our daughters did well with a schedule and didn't have problems with weight gain or sleeping through the night. In fact, both slept 11-12 hours a night by their 6th month. My 8 y/o still needs 11 hours. The long hours of sleep help with proper brain development, which is needed for focusing, learning, absorbing and remembering information. Our 8 y/o learned to read at 2.5 y/o and is now reading 5th-6th grade material (assessed by her 2nd grade teacher). I truly believe it was from all the sleep she had as an infant, which has enabled her to be a success in school.
Any book that helps get your baby to sleep through the night is worth reading and following. Many friends and relatives we know have been successful using the babywise book (parent direct feeding method).
If this book doesn't help, try another. They basically have the same concept of having a schedule/routine. However, it doesn't mean your baby's body will follow it right off the bat. You have to be consistent when you wake and feed the baby and after a few weeks of consistent feedings at a certain time, your baby will start to follow the pattern.
Good luck!