Meaning of "make way with himself"?

Solution 1:

To make way with oneself is an archaic phrasing meaning "to commit suicide". From The Folk and Their Word-lore: An Essay on Popular Etymologies (1904) by A S Palmer:

Somewhat similarly our American cousins sometimes say that a thief "makes way" with his booty, and that a suicide has "made way" with himself....

Today we'd say that a thief gets away with someone else's property and that a suicide does away with himself.