squashimodo, sympathies, it's really hard isn't it, especially when you're told before the birth that 'breast feeding is easy'.
My babies all dropped away hugely from their birth weights - I can tell you about each of them if it's helpful.
Ds1 - born 9lb12. At 10 days he was 8lb10. He simply hadn't been feeding enough to stimulate the milk, and I wasn't someone 'gushing' with milk. The mw suggested expressing to help increase the milk, but I found the whole thing too overwhelming, and was getting really distressed by it all. I ended up supplementing with formula, but he did b/feed until he was 13 months. I always felt a bit of a failure
Dd - born 10lb0. She dropped to about 9 and a half pounds by 4 days, but I had been determined not to repeat ds1's experience and had been feeding her every 2 hours. She was also a homebirth, which helped as I could just stay in bed with her. She started picking up, and although she took a good 6 or 7 weeks to get back to birth weight, she was fine, and was exclusively b/fed to 6 months, carried on b/feeding to 14 months.
ds2 - born 10lb2. Again I fed him every 2 hours. However he did drop by about a pound, and I could NOT get him to put on weight. He had maybe 2 supplements of formula (sometimes they need it because they don't have enough energy to actually b/feed and it can become a vicious circle).
I then got an expressing routine going - which was a PITA but worked! I would express as much as I could get off one side, a little bit off the other (the idea being that as milk becomes more calorific as you progress through the feed, that he would be getting the more calorific milk quicker). Then feed him off the side that had only had a little taken off, keep switching till he really could take no more, then give him the expressed milk as a supplement. Then wash everything, sterilise, and 2 hours later (2 hours start-start) start again with the expressing.
it was really really hard work, but apart from the 2 formula supplements he was exclusively b/fed to 6 months, and fed to 15 months.
As you're 4 weeks, you may need to supplement with formula while you re-establish the milk supply. Can you take a few days to just stay in bed with the baby and feed as often as possible?
Good luck - it can be so hard I know, but you'll get through it!