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"rough sound of the letter -r-" (especially that common in Northumberland), 1760, later extended to "northern accented speech" in general. Possibly the sound of the word is imitative of the speech peculiarity itself, or it was adapted from one of the senses of bur (q.v.), perhaps from the phrase to have a bur in (one's) throat (late 14c.), which was a figure of speech for "feel a choking sensation, huskiness." OED says the Scottish -r- is a lingual trill, not a true burr.
Variant of bur.