"Chestnut weevils" do in fact attack acorns, and hickory nuts such as pecans as well. The species you're dealing with is most likely
Curculio Nucum although it could be any of the
Curculio species. The adult weevils lay their eggs on the developing nuts while they're on the tree, and the larvae eat the nuts before boring out and dropping to the ground, where they remain until maturing into adults.
There are two main biocontrol methods against the weevils. The first is
Heterorhabditis Indica which is a nematode you can buy from various suppliers and which attacks larvae in the soil. The other is
Beauveria bassiana, a fungus which is used to control various different insects and has been found very effective against Curculio larvae if applied to soil, and adults if it's sprayed on developing nuts. The main problem is that, while you could easily kill off the larvae around your own trees, if they have natural habitat nearby they'll quickly return. If you spray beauveria on the developing nuts, you could infect adults and get them to carry the disease around, but it'll probably be an uphill battle either way.