Delk
A surname of uncertain origin, probably a shortened form or regional spelling that developed from older local-name or nickname forms.
The #6,498 most common surname in the United States (2010 Census) — about 1 in every 59,124 Americans shares it.
Etymology
The historical evidence for Delk is thin, and the surname does not have a secure, widely accepted derivation. The 19th-century material you provided mainly shows Delk as a recorded surname form rather than explaining it, and one source appears to treat similar forms as local or dialectal developments. On balance, Delk is best handled as an English surname of uncertain origin, possibly arising through reduction or alteration of an older surname form.
History
The surname is documented in English-language records by the early modern period, and later appears in American records as well. Its relatively low frequency today suggests it remained a minor surname line rather than a widespread one. Because the surviving evidence is sparse, any deeper history should be treated cautiously.
Origin
Regions
Variant spellings
Fun fact
Delk is uncommon enough that even older surname dictionaries seem to mention it only in passing rather than giving it a full entry.
From the historical record
“it is clearly local William Delk>we, 00. Wilts, 1^73. A. William Delhoo, co. Orf., ibid. Walter Dclho, co. Herts, ibid.”
— A Dictionary of English and Welsh Surnames (alternate scan)