From about 32wks with DD and 30ish wks with DS, I consistently measured bigger than dates. With DD, they said she would be a fairly large baby, but never told me how big they estimated. At about 37wks, I had a growth scan with DS as he was consistently measuring a few weeks ahead. They told me I would most likely have a 5kg baby.
DD was 3.6kg, born at 37+3wks and DS was 4.2kg, born at 41+2wks. No they weren't small babies, but not the 5kg whoppers I had in mind either! Plus I birthed both of them vaginally, and DS was a totally natural birth. I am not a large person (as in bone structure, lol!) being only 163cm tall. But my DH is pretty big!
Personally, I don't think fundal height is very reliable. But I'm not a professional nor do I know anything about it, except my own experiences, lol!