Wally Weaver was a research assistant working at Gila Flats Test Base under Professor Milton Glass. When Jon Osterman arrived to start his new job on May 12, 1959, Wally was the one assigned to show him around. During the tour, Wally introduced Jon to Janey Slater for the first time.
In August 1959, Wally was present outside the test vault, along with Milton Glass, when Jon Osterman was accidentally disintegrated during an experiment to remove the intrinsic field from a concrete block. Later in the year, on November 22, he was with Janey Slater in the cafeteria when Jon Osterman finally rematerialized as the super being later known as Dr. Manhattan.
In 1963, shortly after John F. Kennedy's assassination in Dallas, Jon admitted to Janey that he could see the future but could not change it. As proof, he said that they would make love after Wally delivered a pair of earrings that Jon had bought for Janey. Indeed, moments later, Wally arrived at the door with the earrings, which were shaped like hydrogen atoms, thus proving that Jon was telling the truth.
Wally's nickname, "Doc Manhattan's Buddy", and the fact that he is depicted as wearing a bow tie, are quite likely references to "Superman's Pal" Jimmy Olsen.