Everyone associates big-eye takes with Tex Avery. He didn’t invent them, but he mastered them after he arrived at MGM from Warners in 1941. And others borrowed from him.
Here are some examples from Dog Trouble, a 1942 Tom and Jerry cartoon directed by Bill Hanna and Joe Barbera. The cartoon features great expressions that run the gamut of emotions, which is no doubt part of the reason the series was so popular. Here are some of the wilder takes.
These next five drawings are consecutive, drawn by Irv Spence and his assistant (John Liggera?). The cross-eyed drawing seems to have been a popular choice with Spence; he used it at Warners under Avery.
Incidentally, this cartoon was started before Avery arrived at MGM.