this is my first time doing this so hopefully this makes sense. This is such a difficult subject to answer and there are many opinions. 3 weeks is very young still and one perspective is that she was in your tummy for 9 months so it takes awhile and some babies just need the contact. I know that doesn't help when you are exhausted but this too shall pass. Just a couple of thoughts...1. ensuring that she actually has fed enough as she may be still hungry. some babies do feed more at night - they don't understand the difference between day and night. perhaps making sure she is feeding enough during the day. at 3 weeks none of my 3 children when for 4 hours at night (I know others may disagree). it may be worth, at night in particular, just checking that latch is good and a solid feed. I am guessing all the signs are good that she is taking in enough in 24 hours. it may be that you will just need to work on making sure the day feeds are enough 2. keep her warm - which you have mentioned 3. work on the swaddling, this really does help at this age. 4. this may be really contentious but look into co-sleeping. this does work as I had to do it with one of my 3 and I finally got some sleep, but please research this before you do it.
My 3 wk old only sleeps well in her sling (during day) or on us (at night). This is playing havoc with our sleep as I can't really put her down so I can sleep when she does during day (she just wakes uo, even if she was dead asleep when I put her down). At night, she will eventually go down swaddled in her co-sleeper crib, but only after lots of rocking and then not for very long (even though her feeds have begun to space out, so I know she can go 3-4 hrs btw feeds), so that only gives me 30-60 mins sleep at a time before she wakes up and the feed-settle-put down cycle starts again. I've tried sssh-patting her in crib, just putting her down even if she's not asleep and letting her suckle on a finger for comfort. But, she still gets restless quickly, escapes from her gro-swaddle blanket and wakes up... We've also tried various sleeping covers, inc simple blankets, a woombie, a merino 'snuggler' and non seems to make much difference. Although we have figured out she likes to be kept very warm in order to sleep.