Monte Neil was in fifth grade when his father, Glenn, opened WeekEnds BBQ in 2007 in Plainview, 45 minutes north of Lubbock. “When we started it, we didn’t know the first thing in the world about barbecue,” Neil said. “It was just something to do on the weekends,” he added, hence the name. His father is now semiretired, and Neil runs the joint, which moved to the other side of town in February. He added a unique smoker to the new pit room and tweaked the recipes. Now he has a barbecue gem on his hands.After his college days at Texas A&M University, “I didn’t want to move back to West Texas,” Neil said. He took a sales job in Houston after graduation and thought…