Here is a veru small list of papers. Some are outdated but still good information. Do your homework and follow the trail.
Bergström, J. and C. Wiklund. 2002. Effects of Size and Nuptial Gifts on Butterfly Reproduction: Can Females Compensate for a Smaller Size Through Male-Derived Nutrients? Behavioral Ecology and Sociobiology 52:296-302.
Bissoondath, C. J. and C. Wiklund. 1996a. Effect of Male Mating History and Body Size on Ejaculate Size and Quality in Two Polyandrous Butterflies, Pieris napi and Pieris rapae (Lepidoptera: Pieridae). Functional Ecology 10:457-464.
Bissoondath, C. J. and C. Wiklund. 1995. Protein-Content of Spermatophores in Relation to Monandry Polyandry in Butterflies. Behavioral Ecology and Sociobiology 37:365-371.
Boggs, C. L. 1986. Reproductive estrategies of female butterflies: variation and constrains on fecundity. Ecological Entomology 11:7-15.
Braby, M. F. and R. E. Jones. 1995. Reproductive Patterns and Resource-Allocation in Tropical Butterflies - Influence of Adult Diet and Seasonal Phenotype on Fecundity, Longevity and Egg Size. Oikos 72 :189-204.
Cratsley, C. K., J. A. Rooney, and S. M. Lewis. 2003. Limits to Nuptial Gift Production by Male Fireflies, Photinus Ignitus. Journal of Insect Behavior 16:361-370.
Gage, M. 1994. Association between body size, mating pattern, testis size and sperm lenghts across butterflies. Proceedings of The Royal Society of London. Serie B. 258:247-254.
García-Barros, E. 2000. Body size, egg size, and their interspecific relationships with ecological and life history traits in butterflies (Lepidoptera: Papilionoidea, Hesperioidea). Biological Journal of the Linnean Society. 70:251-284.
Oberhauser, K. S. 1997. Fecundity, Lifespan and Egg Mass in Butterflies: Effects of Male-Derived Nutrients and Female Size. Functional Ecology 11:166-175.
Watanabe, M., M. Bon'no, and A. Hachisuka. 2000. Eupyrene Sperm Migrates to Spermatheca After Apyrene Sperm in the Swallowtail Butterfly, Papilio Xuthus L. (Lepidoptera : Papilionidae). Journal of Ethology 18:91-99.
Wiklund, C., B. Karlsson, and O. Leimar. 2001. Sexual Conflict and Cooperation in Butterfly Reproduction: a Comparative Study of Polyandry and Female Fitness. Proceedings of the Royal Society of London Series B-Biological Sciences 268:1661-1667.
The weight of butterflies and moths can be influenced by the size of the individual. Larvae reared in the laboratory, the specimens that consume little food are smaller than those well fed. There are also differences in weight of males and females, females are larger and heavier than males. In the pupae you can also determine the sex because females are heavier than males.
Is there a special reason why you want to know the weight of adults? of how many species? There are so many different sizes among the thousands of "butterfly" species existing. It is easier to weigh the pupae. After a rearing attempt you can give exact data out of 30 or 100 pupae. Most often, pupae can already be sex determined, observing the last abdominal segments. Is it for biomass appreciation?
It would be interesting to know in what way you are interested in butterfly weight (that is, what you would like to do), there are quite a few papers on butterfly size... Alfredo's answer includes quite a few examples.
Dr. Paul Opler states, "I have some information on butterfly weights but not exact weights for the largest and smallest butterflies. However, I can make pretty good guesses. I have weights ranging from 0.3 gram for a large swallowtail to 0.04 gram for a small butterfly called the elf. My guess is that the female Queen Victoria Birdwing, the world's largest butterfly, would weigh 2 or 3 grams and one of the World's smallest butterflies, the Pygmy Blue, would weigh only a few thousandths of a gram."