Originally, Leatherface was just another gimp amongst a famiy full of retarded cannibals. The sub-text strongly suggested the Sawyer Family was inbred. They preserved their elderly in some form, possibly by bloodbaths. Later installments built upon these tropes, often paying homage to them in some way.
The first sequel had the Sawyer Family running a chili outfit, using human flesh for meat. Leatherface appears to fall for a radio DJ and a bizarre sex scene involving the chainsaw ensues. Texas Chainsaw Massacre Part III finds Leatherface just one of many Sawyer Family badasses with a Neo-Luddite grandmother who paradoxically speaks through a voicebox. Later reboots and remakes tend to focus on younger characters, some of whom are related to Leatherface in one form or another.
Hooper said the character and movie were inspired by Ed Gein and his crimes.