SOH Perhaps I am paraphrasing, but certainly this was the advice I and everyone I spoke to received from health visitors - that's not even counting some of the terrible advice, like I was advised to wean at 4 months because of a misplaced dot on the weighing chart, and a friend was advised to start with quavers. WTF?
NHS advice is "around six months", WHO says "If complementary foods are not introduced around the age of 6 months...an infant’s growth may falter." and UNICEF Baby Friendly uses the NHS definition of "around six months" too.
So you are right that these three official bodies don't use "by".
But popular sources of information have a mixture:
Babycentre says "By about six months, you'll probably start noticing signs" (and lists one of the signs as "looking at you while eating" FFS)
Gina Ford says "if you decide to wait until six months..." as though it's a rare thing. She also talks about iron deficiency, saying "Remember the iron stores a baby is born with have been depleted by the time he reaches six months"
Cow and Gate and SMA are surprisingly sticking firm to the NHS wording of "around six months". Aptamil does even better by using language like "from six months".
Hipp takes a definite chair on the side of "by" with this statement: "Even if your baby shows no signs of wanting to begin weaning, it is still best to make a start at 6 months since this is an important step in their development. Delaying weaning may also mean that your baby doesn't get enough of some important nutrients such as iron."
Bounty is similar, using the phrase "By six months" and "Why six months is bang on" and includes a tale of a mum starting at 5.5 months because her baby didn't sleep well.
Boots' article is well informed and says "at six months". So does Netmums' article.
First google result on google UK for early weaning was this: www.madeformums.com/baby/is-it-safe-to-start-weaning-at-4-or-5-months/36085.html
And a daily mail article (I know, but it has a wide readership) claims "Babies weaned after six months are 'three times as likely to develop type 1 diabetes'"
It's not so much what the message is, but what people are hearing, if that makes sense?