Weaver was a member of the United States Marine Corps before he became a professional boxer. During his tenure in the Marines, Weaver was able to obtain heavy built muscles. Because of that, he was nicknamed Hercules as a boxer. Just like in Carlos Palomino's case, Weaver was a resident of California since a young age, therefore, many boxing fans actually thought of him as a native Californian.
Throught most of his early boxing career, Weaver was seen merely as a journeyman, title given to boxers who will often travel, mostly on short notice, and lose to young prospects or fading former world champions for a few hundred dollars. In his first two fights, in 1972, he lost to Howard Smith. The only difference between Weaver and other journeymen was that most of Weaver's fights took place in California at this early stage of his career.
He built a record of 14 wins and six losses, with 8 knockouts, before challenging Stan Ward on January 24, 1978, for the California state Heavyweight title in Sacramento. Weaver lost a 12 round decision, and then on August 19, he was defeated by Leroy Jones in Las Vegas for the North American Boxing Federation's (NABF) belt. But he won three in a row by the end of the year, and on January 18, 1979, he and Ward had a rematch, with the United States Heavyweight title on the line. Weaver won by knockout in round nine, and he won two more bouts, catching the eye of WBC world Heavyweight champion Larry Holmes, who gave Weaver a chance at the world title on June 22 of that year, at the Madison Square Garden in New York City.
By this time Weaver had a record of 21 wins and 8 defeats, and many, including Holmes' management team, still thought of him as a journeyman. Weaver proceeded to drop Holmes in round four, however, and gave Holmes what many fans considered to be a spirited struggle before being dropped in round eleven and succumbing to the world champion in round twelve by knockout. Weaver got two more wins, including one over Scott LeDoux, before the decade of the 1970s ended.
On March 31, 1980, Weaver was given a second chance at becoming world Heavyweight champion when he faced WBA world champ John Tate in Knoxville, Tennessee. Weaver was trailing on all three scorecards going to the 15th and final round, meaning he would need a knockout to claim the title. With 45 seconds to go, he connected with a right that sent Tate to the canvas face-first. Tate was not able to get up, making Weaver the WBA's world Heavyweight champion. For his first defense, he travelled to South Africa, where he recovered from an eighth-round knockdown to defeat future world champion Gerrie Coetzee by knockout in round thirteen.
His third defense actually took more than one year to take place, and it was one of boxing's most controversial fights of the year. On December 10 of 1982, he faced Michael Dokes. Dokes dropped Weaver within 30 seconds of the opening bell, but Weaver got up and was apparently recuperated when referee Joey Curtis abruptly stopped the bout. Weaver's camp protested, and a long investigation by the WBA followed. Curtis had apparently been affected by the recent death of South Korean boxer Duk Koo Kim after a fight with Ray Mancini, and he stopped the fight fearful that Weaver would get badly hurt too.
A rematch was appointed, on May 20, 1983, at the Dunes hotel in Las Vegas. In the first occasion that two world Heavyweight championship fights took place at the same place and during the same night (Holmes kept his WBC crown at the main event by defeating future world champion Tim Witherspoon) Weaver and Dokes fought to a 15 round draw (tie). Dokes kept the title although most observers felt Weaver deserved the verdict.
In September of that year, Weaver met Stan Ward once again, and he beat Ward by a knockout in nine rounds.
Weaver then started a pattern that really resembled that of a journeyman, winning some fights and losing some for the rest of his career. On June 21, 1985, he had his last serious shot at becoming world Heavyweight champion again, when he lost to the reigning WBC world champ, Pinklon Thomas, by knockout in round eight. After that, he gradually faded away from the list of top rated Heavyweights. He went to Cambodia to fight, and lost fights to former world champion James Bonecrusher Smith and future world champion Lennox Lewis.
Weaver retired after 1998, with a record of 41 wins, 17 losses and 1 draw, 28 wins coming by knockout.