Did you see something where this might be a effective treatment for cherry weevil? I'm just curious, as I can't find anything where it lists neem specifically on weevils.
From Montana State: "Neem is most effective as a foliar spray applied periodically to new flushes of growth. On some species of plants neem also works as a systemic pesticide, absorbed into the plant and carried throughout the tissues, ingested by insects when they feed on the plant. This may make it effective against certain foliage-feeders that cannot be reached with spray applications, such as leafminers and thrips. Neem has some systemic activity when applied as a foliar spray, but it seems to work best as a systemic when applied as a soil drench, absorbed by the plant roots. It is not known how effective neem soil drenches are for larger ornamentals and trees, so drenches are usually recommended for smaller plants."
Plus, not all neem products are the same and concentrations differ. It should also be noted that alkaline soils, which are common in most of Colorado, make the product less effective.
If you are looking for an organic approach, consider using a sticky substance at the base of the tree, like tanglefoot for stickums. Weevils are nocturnal and emerge at night. They crawl up the trunk, and if they get stuck by the sticky substance, they will not be able to feed.
Here's information from the University of California-Davis: http://www.ipm.ucdavis.edu/PMG/r105301211.html#MANAGEMENT
And more information on neem as a drench (and general comments) from Montana State: http://scarab.msu.montana.edu/YardGarden/docs/neem-insect.htm