Unfortunately, few treatments can eliminate this pest because they burrow within the roots of host plants.
It's important to note that Weevils are nocturnal, so you're not going to catch them in the daytime. If you suspect a possible infestation, or, come to find your garden plants have been attacked, but there is no sign of any culprit, you may want to attempt a few evening torch checks. Check on and under the leaves and fruits of plants.
It's thought that good housekeeping, such as practising: mulching, re-hilling, field sanitation, crop rotation and using clean planting material, can significantly reduce the severity of an infestation.
Pheromone traps can be used to monitor pest populations in the garden.
Likewise, Diatomaceous earth dusted over leaves and around the bases of plants can kill Weevils. Be careful during application, as this stuff is nasty if inhaled and can be extremely irritable when in contact with the eyes.
If available, beneficial nematodes can be bought online and watered around desired plants. This can be effective for up to 4 months and will eradicate any grubs hiding in the soil.