Research Notes:
The biography of William de Burgh in the Oxford Dictionary of National Biography states that William de Burgh was the brother of Hubert de Burgh, justiciar of England, the father of Richard de Burgh, lord of Connacht, and ancestor of the de Burghs, earls of Ulster, and suggests that he may have had a marriage alliance with the Ó Briain of Thomond. [1]
According to one Irish source de Burgh was married to a daughter of Domnall Mór Ó Briain, which is consistent with the fact that he was frequently accompanied by his Ó Briain allies, hereditary enemies of the Mac Carthaig and the Ó Conchobhair, in his numerous campaigns in Desmond and Connacht.
[1] C. A. Empey, "Burgh, William de (d. 1206)," Oxford Dictionary of National Biography (Oxford University Press, 2004, online edition), [Oxford_Dictionary_National_Biography], [OxfordDNB(UM)].