Why the amazement, GourmetM?
Pork was the commonest protein in early America, particularly in the South. One reason being that when it comes to self-sufficiency, no other domestic animal is as good at it. Typically, pigs were turned loose in the woods, to fend for themselves. Thus the saying, "root, hog, or die."
Such is still the case. Some states, like Florida and Texas, are covered up with feral hogs. And it's getting to be a real problem here in Kentucky. Plus there's a population of true wild boar in western North Carolina.
But pork was common in the old world as well. Hannah Glasse's book---which, btw, went through 20-something editions---was actually English. In fact, all cookbooks used in British North America were either published in England, or reprinted here, until 1796, when Amelia Simmons published American Cookery, which is considered to be the first American cookbook.
What surprised me, when I first read that recipe, was the use of the word "barbecue." I somehow had it in my head that it was a relatively young term. As it turns out, the word was used as early as the 1500s. Notice, too, that she uses it as a verb, whereas in the South, today, it's mostly used as a noun. That is, grilling is what you do. Barbecue is what you eat.