My very limited understanding regarding the name in South Africa is that there were two Weyer (to graze - herdsman?) family lines in the Cape in the 1700s, one Hendrikz Weijer from Limburg province, Netherlands and later Stephanus Janse Weÿers of Groningen, Netherlands.
As to the Weyer family name, by 1650, the name was spread throughout Europe including France and Poland. An example of limited records from Holland for this period (church records there only started circa 1550-1600):
Name Role Event Date Place Source
Abraham Schorteijn Weyer Beluid Vermeld 07-12-1675 Sneek Church burials
Abraham Weyer Second party Notarial deed 28-11-1678 Notarial records
Abraham Weyer, vader Constituant Notariale akte 10-08-1664 Notarial records
Adriaan Mels van de Weyer Father Baptism 03-04-1667 Breda Church baptisms
Albert van Overmeer, zoon van + Weyer van Overmeer
Constituant Notarial deed 11-03-1696 Notarial records
Alexander de Weyer Father Baptism 22-07-1685 Bergen op Zoom Church baptisms
Anna Weyer Registered Marriage 18-07-1722 Dordrecht Church marriages
Anna Willebrordi van de WeyerWitness Baptism 20-07-1690 Vlierden Church baptisms
Anna Willebrordi van de WeyerWitness Baptism 20-07-1690 Vlierden Church baptisms
Anna van de Weyer Witness Baptism 19-03-1721 Lieshout Church baptisms
Afrikaans? Just a Language?
As to "white" "Afrikaners" (if I have ANY right to voice a humble opinion), methinks that they are culturally not the same as Europeans insofar that there was a strong sense of alienation from and persecution by Europeans/English (eg Huguenots being persecuted from at least 1572, Dutch taxes (“opgaafrolle”) in the Cape, Batavian Republic and then the English from 1814ish).
Life in Africa in the 1700s being very different to that in Europe leading to descendents being African.
In addition, Scottish animosity against the English following the defeat by Charles 1 was very strong, and that influence came through to the later people of the western Cape and Trek Boers (oppressed by English colonisers) via their Scots pastors in the earlier 1800s (Thom, Murray, Reid etc.) thus contributing to Boer nationalism, a separate identity and a formalised language.
There are many similarities with the oppressed Acadians (Cajuns) who were equally divergent and alienated from Europeans and who forged a new life from scratch in Louisiana .