The variant “Hoheweg” is from a record about one of the oldest families I found, formerly located at the “St. Sylvestri und Georgii” church in Wernigerode in the Harz region of Germany. Father of this family was the “Kanngießer/Kandelgießer” (pewterer) Jacob Howeg, whose daughter Catharina was born on the mentioned date.
Jacob himself died in 1638 at the age of 75, when both of his sons Heinrich and Jacob Jr. were already naturalized as citizens of Wernigerode. Due to some unknown circumstances (maybe because of the 30 years war and the high death rate), he was buried at the graveyard of another church in Wernigerode called “St. Nicolai”. So far his family seems completely isolated to the bigger Howeg branches despite the local proximity to Oschers- and Hadmersleben.
“Hoheweg” is an interesting variant as it is fairly close to the way the original meaning would be spelled nowadays, e.g. someone saying “Dort ist der hohe Weg” (there’s the high way).