Meza was a popular fighter among Latin Americans, specially those of Mexican descent who lived in North America.
Meza lost for the first time on his second bout, being beaten on points after four rounds by Valentin Holguin on October 13 in Los Angeles.
But, in his next fight, on November 18, he lost by a four-round decision to Carlos Ortiz, (not to be confused with the Puerto Rican world champion boxer and Hall of Famer of the same name) in San Diego.
Meza began rising in boxing's ranks when he knocked Ortiz out in the first round on December 16, also at San Diego.
Meanwhile, Meza returned to boxing on April 26, 1983, knocking out Roberto Castillo in four rounds at Las Vegas.
On August 18, he and Lupe Pintor squared off in a fight that garnered major interest among Mexican boxing fans.
Meza lost his title in Tijuana that night, when Pintor dropped him twice, outpointing him over twelve rounds.
[3] Pintor lost his title, in turn, to Samart Payakaroon, who gave Meza a chance to recover the WBC world Super Bantamweight championship on December 10, 1986 in Bangkok.