This is all fascinating and I'd love to know details of our connection through the puritan, Humphrey Davie.
My cousin, Sir Patrick Ferguson Davie 5th Bt asked the College of Heralds to investigate the Bardolph connection in the 1950s or sometime soon thereafter - in particular to assess his chances of establishing a claim to the abeyant barony of Bardolph (see Burke's Extinct Peerages). The Herald he employed (Colin Cole?) advised him that any claim would now belong to the Duke of Norfolk.
Robert Davie's son John Davie (1541/2-1612) applied for the right to bear the arms of Bardolph (his maternal grandfather’s family – azure, three cinquefoils or, on a chief of the second a lion passant gules) and he was granted this right on 20th April 1594. (He also adopted the halcyon bird crest, which had been granted by Dom Antonio, the pretender to the Portuguese throne), but he did not augment his arms with the ensign of Burgundy (his grandfather’s canton).
The decision to claim the arms of his mother’s family reflected the noble ancestry of his mother’s family and demonstrated his superior lineage to his older half-brothers. Had he, as a younger son, decided to claim his father’s family’s arms (de la Wey) he would have had to add a mark of cadency; this would have reflected his lowly ranking among his siblings. It is also possible that he might have harboured an idea of trying to claim for himself the ancient, abeyant barony of Bardolph (which my cousin Sir Patrick FD investigated in the 1950s or thereabouts).
We still use both de la Wey and Bardolph escutcheons on our coat armour, but the Bardolph coat alone is shown as the main escutcheon on John Davie's memorial in St Mary Arches church in Exeter (and on the memorial in Sandford Church to his daughter-in-law, Juliana Strode). This memorial also includes the arms of Owlacombe and three smaller shields, which impale the arms of de la Wey and those of his two wives, Willmot Peter and Margaret Southcote. It was erected by his son, Sir John, who quartered the arms of de la Wey and Bardolph for the first time, doubtless because he needed to prove his own entitlement to coat armour and this is the way the arms have appeared ever since.
John's son (Robert's grandson), Sir John Davie (1589-1654) had to have a pedigree drawn up at the time to be eligible to become a baronet (1641) and this was duly produced and dated 1647, and it states that John Thomas’s descent from “the noble family of Bardolph” was recorded by Sir Gilbert Dethick (Garter King of Arms) “in his own writinge”. This pedigree is now in the West of England Studies Centre in Exeter - sadly it is in very poor condition thanks to the fire at Creedy in 1914.
The connection with the noble family of Bardolph is interesting, but unfortunately I don’t know any more about it - although I think we must assume it does exist and that William Bardolph and his daughter, the wife of John Thomas of Tichfield, emanated from a junior branch of the noble Bardolph family.
There is only one family called Bardolph that I have found in Hampshire from early days; and they held the manors of Greatham, Emsworth and Warblington, which their ancestors had inherited in 1286. The family owned these properties for only about a century and there is no mention of Tichfield. As you will know, the principal Bardolph family died out in 1408 when the 5th Lord Bardolph was mortally wounded at Braham Moor in the rebellion against Henry IV. Bardolph was declared a traitor, his property was sequestered and his remains were ordered to be quartered.
Somewhere along the way something led me to suggest that John Thomas alias Bardolph of Titchfield who died (as you say in 1529) might have been born in 1489. Also that his wife's father was called William and that he may have died in 1508.
It seems that you have discovered quite a lot that casts a doubt on what has been accepted for many years. I would like to be kept in touch with any developments. Please.