My daughter is nearly 6 months old. but she was 10 weeks early. so this little dink of a thing...she she sleeps though the night. I dont ever let her cry anything out on her own and we also co slept for a while as she needed us. and after what she had been though, we let her have us when she needed us as we couldnt be there sometimes.
There is nothing wrong with BFing him still!
Now, Alice does sleep though the night. She power feeds in the evening! I always ALWAYS get her well fed, get her up on my chest and burp/cuddle her to sleep. then gently lay her down in her moses basket. IF she fusses I rock her and rub her back...she then goes to sleep...if she doesnt, I get her up, more comfort, more suckles, more snuggles and THEN she will go down. He is only little still. if he needs you he needs you. IF you want to give up the BFing then dont put him to your breast during the night to settle him. its funny though, when she came home at 4lbs...she was on 4 hourly feeds!
IF it was me...I would give him a bottle and cuddles and then lay him down. if in a cot, have your hand on his back or bum..you can pat or just lay your hand...when I do the pat and rubbing...I gently over a minute LESSEN my pressure on her...so its not..im here, now im gone! if its done slowly she doesnt notice as too busy sleeping!
It is funny though how he slept in hospital...but...he was poorly!!
I would suggest giving him a bottle top up...even if expressed milkies or formula to really TOP him up! so he wont have hunger keeping him away, also it might help bring up a big lump of wind...and therefore sleep better and longer 
Also...if he wakes up...dont talk to him. just tend to his needs without talking to him and stimulating him xxx