The larvae may damage roots or chew bark at the soil level and can be particularly troublesome on plants in containers. Handpicking the adults off the plants is one way to reduce the population. They feed at night. Look after dusk with a flashlight, and drop the small brown adults into soapy water. Any adults that are killed now will reduce the later populations.
Some people spread sheets under the plants and shake hard, the dispose of the fallen weevils.
The adult weevils will climb up to the new spring growth, gnawing on it. Wrapping the trunk of the plant with nontoxic sticky substance such as Tanglefoot will sometimes help to catch the critters as they emerge from the soil and start up the plant for their leaf dinner. Wrap some clear plastic cling wrap around the trunk of the shrub, then spread the Tanglefoo t over the wrap so it isn't directly on the bark. The wrap should be tight enough so beetles can't crawl under it. Other gardeners have also tried teflon tape wraps, about 4 inches wide, which tend to be so slipper that the beetle falls to the ground.