Hi Judi,
I had problems with some type of exotic citrus weevils last year. During Spring they chewed up the young leaves on my orange trees and by fall they were feasting on older citrus leaves and nearby orchids.
These bugs are hard to kill because they go through several stages of growth/development. Part of their life is spent eating roots underground. As they mature they move above ground. The growth cycle takes about 5 weeks. I couldn't find any documentation on foolproof treatments. My type of weevil is not native, and began showing up in Florida a few years ago. The professionals are still working on effective treatments.
My early treatment was neem oil and it didn't phase them. My trees never set fruit so I moved on to stronger treatments that weren't recommended for citrus. One of them was a systemic insecticide made by Orthene or Orthenex. The systemic did not kill the bugs on contact but I was hoping it would later kill anything munching on treated plant tissue. I then used Ortho Max on my entire lawn. Despite my efforts there were more weevil sightings. Finally, I used a product called Raid Max. This product has several weeks of residual effect and is recommended for indoor use. I thoroughly sprayed my trees with it and it killed those nasty critters on contact.
This spring my citrus trees have new leaves, and the blooms are successfully setting fruit. So far, I haven't sighted any fully developed weevils, but as a precaution I did a repeat yard treatment with the Ortho Max, and will continue to monitor on a daily basis.
I hated using poisons, but couln't find a better effective alternative. Successful treatments must be aimed both above and below the ground. You might have other host plants growing in your yard. Check all of your plants for the tell-tale sign of notched or folded leaves. There was a list of 80+ plants that my citrus weevils were attracted to.
Good luck with your battle.