In 1985-1986 he made infrared observations of Comet Halley from the NASA Kuiper Airborne Observatory (KAO), which resulted in the first unambiguous detection of water in comets. For this latter work, he was awarded the NASA Medal for Exceptional Scientific Achievement in 1988.

During the past decade, he has led many investigations of comets using the NASA/ESA Hubble Space Telescope (HST). Weaver was the Principal Investigator (PI) on the first HST spectroscopic observations of a comet in September 1991, which resulted in the discovery of the CO Cameron bands, a unique tracer of CO₂ in comets. He was the PI on the main HST program to study Comet D/Shoemaker-Levy 9, which plunged into Jupiter's atmosphere in July 1994, and he also served as the Chair of the Science Observing Team, which oversaw the entire HST Comet-Jupiter impact campaign. For this latter work he received a NASA Group Achievement Award. He also led HST investigations of Comets Hyakutake, Hale-Bopp, C/1999 S4 (LINEAR), and several others, and he is a member of the team using HST to measure the sizes, shapes and colors of cometary nuclei.

Weaver is currently participating in a program to study comets with FUSE; more than 60 new emission features have already been discovered during that investigation, including the first detection of H₂.

In parallel with his UV studies, Weaver has also continued his infrared and radio investigations of comets, using ground-based facilities at the IRTF, Keck, JCMT, CSO, and IRAM observatories.

During the summer of 1996, asteroid 1984 FN was renamed to asteroid "Halweaver" in recognition of Weaver's work on the chemical composition of comets.

Weaver has published over 90 papers, including studies of planets and their satellites in addition to comets. He has a longstanding interest in research on the formation and evolution of planetary systems and, in particular, wants to investigate possible connections between cometary matter and interstellar material in star-forming regions.