Oh if your urine was diluted that's a no brainer - CB are shit for diluted urine. The sensitivity is one of the weakest out there. Also, remember you're not 100% sure on dates - a few of us in my antenatal group have been put back as far as a week! Try to relax, although I worried at the 5 week mark and to be honest, still have anxiety (this is my first).
GP's won't routinely provide early reassurance scans ad-hoc, you only really receive one of those if you've got bleeding and pain, and even then due to how early you are sometimes you'll be told to come back a week later. At 5 or so weeks, even if you did have a scan, you wouldn't necessarily be able to see anything. I had an emergency scan at 6 weeks 3 days (bleeding/pain) and we were fortunate enough to see the heartbeat, but we were very lucky.
Also, chemical pregnancies are common in the sense that a lot of women don't even know they've had them. From what I've read but please don't quote me, the fact your little bean is registering as 2-3 weeks on a CB suggests bean has implanted and is growing, and unless you see blood or pain that would suggest a miscarriage, you should be fine and ignore the CB tests. From this point onwards I'd say you move from having a chemical pregnancy to, if anything DID go wrong, having a miscarriage, but the signs and symptoms of the miscarriage would be blood, pain and if ectopic, localised pain on one side. Unless you're experiencing those, please try to relax
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Lastly, join your antenatal "topic" on Mumsnet - I'm guessing you'll be due in December? Join the topic, there will be other Mum's in the same position as you - me and my October Mum's talked about everything 