The surname Arthur obviously stemmed from the first name. It was found in various parishes up and down Cornwall in the 1500s. As the name of the great Celtic mythical warrior it’s interesting that it was no more likely to be found in the Cornish-speaking than the English-speaking districts at that time.
Aver presumably derived from the more common Avery in one Cornish parish.
If you want to compare these distributions with the nineteenth century position see here.
Cornish studies resources 