In today’s English, barbecue is the usual spelling of the word with several senses related to the cooking of food over open fire. It’s the spelling that tends to appear in edited writing, and it’s the one that dictionaries note first, for what that’s worth (and some don’t note any other spellings). Barbeque is a secondary spelling that appears especially often in the names of restaurants and products. It has steadily gained ground over the last few decades, but it is still far less common than barbecue overall.
The word has been spelled several ways since coming to English from the Spanish barbacoa in the 18th century (its earlier origins are fuzzy, though the conventional wisdom is that the Spanish adapted it from a term used among Caribbean natives).1 In the OED’s historical examples there are barbecu, barbacue, barbicu, and babracot,2 and today there are several abbreviated forms, including bar-b-q and just BBQ. Despite the many forms, barbecue gained clear ascendancy in the late 19th century, and it has gone unchallenged ever since.3
Their court commenced on the next Monday, as the barbacue was on a Saturday, and the candidates for governor and for Congress, as well as my competitor and myself, all attended. [A Narrative of the Life of David Crockett, Davy Crockett (1834)]
When the Guiana Indians have killed a tapir and roasted its flesh on a babracot, they take good care to destroy the fireplace. [The Supernatural, John H. King (1892)]
The Whig barbecue came off first, and no man ate more and carried off more ham and barbecue, in his basket, than did Jonas. [Whitaker's reminiscences, R.H. Whitaker (1904)]
A barbecue party can be formal if you like, but everyone is happiest when dirtiest, and blue jeans are a perfect costume for sitting on earth or stones. [The ABC of Barbecue, (1954)]
Today, Brooks, 51, has two barbeque restaurants at Intercontinental Airport and one at Hobby Airport, and he has a mobile food court at the George R. Brown Convention Center. [Black Enterprise (1996)]
Also present will be face painting, readings, dance and a bar-b-q with hot dogs, hamburgers, sno-cones, and beverages. [Verde Independent (2013)]