Booming production of oil and natural gas has exacted a little-known price on some of the nation’s roads, contributing to a spike in traffic fatalities in states where many streets and highways are choked with large trucks and heavy drilling equipment. An Associated Press analysis of traffic deaths and U.S. census data in six drilling states shows that in some places, fatalities have more than quadrupled since 2004—a period when most American roads have become much safer even as the population has grown. “We are just so swamped,” said Sheriff Dwayne Villanueva of Karnes County, Texas, where authorities have been...