hi S.;
i hope i'm not beign repetitive but here are the things i would try, having a 3.5 yr old and a 21 mo old.
first of all; if you are bottle feeding and not nursing, try some different bottles. the fast flow of many bottles often gives the babies a tummy ache; they may get air in the belly and stop eating so you think they are full, but really they are then just gassy and still hungry. so try a Dr. Brown's newborn bottlle, the 2 oz size and go very slow w the feeding.
also try switching formula. he might be bothered by what you're using.
if you are nursing, google La Leche League Int. and click on 'resources' for your area meeting and chapter leader; call this person right away, thier number will be on the web page. there are a variety of nursing issues that could be going on.
next; this certainly could be colic. if so, you might just have to hang tough till about 3 months, when most colic starts to resolve. i have heard of babies who will cry NO MATTER WHAT all through the middle of the night, so what you're experiencing is within the range of normal for a colicky baby. try getting a sling or Bjorn or a Baby Hawk Mei-tai baby-wearing item; you may just have to tie this baby to your body and keep him there. some of them are like that.
slings and Mei-tais can be found also by checking in with your local La LEche League or just google 'baby slings' or 'mei-tai baby wrap' or 'baby wrap'. lots of stuff will come up. you might need to call the person who makes or sells what appeals to you for instructions on how to use it or ask someone at La Leche.
now speaking of La Leche again, i don't mean to harp on this, but they really are a FREE RESOURCE that has all the up to date info and want to HELP you no matter what, even if you are not nursing; you could certainly call them and say, "Look Im not nursing but i need this other help, what should i do," and they will help you.
i say this because i wonder if your baby might have TOUNG TIE. my son did and his nursing was a disaster for several days at the beginning and he kept losing weight and we were freaked; he also did not sleep. when i had a Lactaction Consultant come to my home she took one look at his mouth and saw the problem; with toung tie the baby's toung is too short for him to eat properly. often times they need a tiny cut to the muscle under the toung; but only someone with a trained eye would know what to look for; many OBGYNS and even peds don't know what to look for. anyway you might get this checked out.
also; it is really safe and fine to sleep the baby in bed with you as long as you do it mindfully and follow some guidlines for safe co-sleeping. try the Dr. Jay Gordon website and look up 'family bed.' at 6 weeks old there are NO HABITS, the babies are not wired that way yet. right now you need to do whatever it takes to get you and the baby more sleep. you might get a molded sleeper, this thing you can put in your bed to keep the baby on his side or back but it''s next to you so maybe he would tolerate that.
another thing to consider is swaddling and side sleeping; neither of my kids would sleep on thier backs so i swaddled them and propped them on thier sides in thier co sleepers next to my bed, using rolled up blankets to stabilize them. you can google 'swaddling' to learn how, or try the Kellymom.com website. your baby might be a little big for it at this point but you could do it just a tad looser, he might like it.
so here are the sites to check
Dr Jay Gordon
Kellymom.com
La Leche League Intl.
and also you can try Dr. Sears and there's always good old Dr. Spock's Baby and Childcare, which is a book we come back to again and again.
lastly i would say consider buying a rocker or glider chair for yourself with a good footstool and see if you can sleep in it holding the baby, especially if you get a sling or a Bjorn or mei-tie where he will be secure.
lots of love and hang in there, one way or another this WILL improve.
J.