The best book I know on English usage is Troublesome Words by Bill Bryson. I don't agree with all of it, mind you; I make it a point not to agree with all of anything, just in case. Yet my thoughts this morning turned to this entry.
barbecue is the only acceptable spelling in serious writing. Any journalist or other formal user of English who believes that the word is spelled barbeque or, worse still, bar-b-q is not ready for unsupervised employment.
Incidentally, a barbecue is a framework of sticks. You can cook stuff on such a structure; but the first use in English, way back in 1697, was to a barbecue bed.
[We] lay there all night, upon our Borbecu's, or frames of Sticks, raised about 3 foot from the Ground
- William Dampier A New Voyage Round the World
Now I must dash as I'm spending the afternoon at a BB-queue.