I had growth scans done because they thought she wasn't big enough! The last one I had was on a thursday and they estimated her to be 2.94kgs an I gave birth on the monday morning, she was 2.95kgs!!
BUT this was the FIRST time I have ever heard of the US estimation being correct!! Especially with "large" babies, they can be quite a bit different to the actual birth weight... The sonographer said it could be out my 300gms each way but really it can be out way more than that!

Your body will not grow a baby you cannot physically birth, so don't worry.. you can do this! And you can birth your perfectly sized baby!!!