Wesley is a scrawny businessman working in the black market. He sells the cattle that Alameda Slim steals for him. Wesley is primarily focused on business and making money. He generally doesn't have any patience for Slim's "unique" ways of stealing cattle and he always tries to get jobs done in a timely fashion.
Wesley first appears towards the end of the film when Alameda Slim and the Willie Brothers return to their hideout in the old mines to buy the herds of cattle that they have stolen. He has a profitable arrangement with Slim, whom he mistakenly refers to Mr. Wesley as "Mr. Weasley." Slim steals cows with his yodeling, Wesley buys them, and Slim uses the ill-gotten money to buy the now-bankrupt farm he stole the cows from. Wesley tries to be punctual and is shown to get very angry when there are any delays. He also reveals that he gave up clown college in a surprised tone after noticing the chaos on the mine shaft. Eventually, Wesley gets beaten up by Maggie, Mrs. Calloway, Grace, Lucky Jack and Buck, and they lock him in a train cart along with Rico and the Willies, who are seen beaten up as well. He was presumably arrested following Slim's arrest by Sheriff Sam Brown, or possibly starved to death along Rico and the Willies in case they were never found.