1580s, "stupid person, blockhead," perhaps from dialectal logger "heavy block of wood" + head (n.). Later it meant "a thick-headed iron tool" (1680s), a type of cannon shot, a type of turtle (1650s). Loggerheads "fighting, fisticuffs" is from 1670s, but the exact notion is uncertain, perhaps it suggests the heavy tools used as weapons. The phrase at loggerheads "in disagreement" is first recorded 1670s.
Engaged in a head-on dispute: “Labor and management are at loggerheads in this affair, and it may be some time before they can negotiate a settlement.”