The research that is being done in the canopy is very varied and the equipment used is also quite variable. Some of the research involves nothing more than a notebook and a pencil, while other projects might require an entire team to get the gear up into the canopy. Most of the projects with which I have been involved were relatively small, usually involving only one or two students and/or researchers and minimal equipment. The most complex project involved the placement of a small portable platform in the canopy which was removed after several days of use.
One of the more interesting projects is a study being conducted by a graduate student from Auburn University and his assistant. The two are collecting data on the eyelash viper, which is an arboreal poisonous reptile. Most of the specimens found thus far have been on low branches and in small trees near the ground. Quite a few, however, have been found high in the canopy, the highest having been found at a height of nearly one hundred and thirty feet. The two researchers capture the specimens, collect data such as weight, length, time of day, height off the ground, type of tree, and so on, then release them again. Many of those captured have been captured before and the database of information on these creatures is growing. The equipment that these two researchers are using weighs in at about ten pounds, not counting their climbing equipment and the equipment that one will usually carry along on a walk in the rainforest.
Another student researcher spent several days in the canopy with nothing more than pen, notebook, and binoculars and documented all the various creatures that she observed in the tree. In three days of observations (more or less) she identified over a hundred different creature, most of which were insects, but including such things as bats, frogs, a snake, and a number of different birds.
To answer the question, all I can say is that the amount of gear necessary depends upon the project itself and there is no set list of equipment.