There are a lot of common names for the native weed Galium aparine (Rubiaceae). They include cleavers, stickywilly, and catchweed bedstraw. Although I find some humor in the name “stickywilly,” “catchweed bedstraw” is probably more fitting since members of the genus Galium are called bedstraws.
Words like “sticky” and “catchweed” in the common names were inspired by the hooked hairs that cover the stems, leaves, and fruit. When you run your fingers up the plant’s surface, these hairs give it a sticky feel. The hairs allow the plant to cling to other plants and objects, providing support for the weak shoots. They also have a role in seed dispersal if they stick to passing animals (Burrill 1992).
Side note: I think the tiny insect on the plant above may have been a shining flower beetle (family Phalacridae) but he got away before I could catch him.
Burrill, L.C. 1992. Catchweed Bedstraw. PNW (Pacific Northwest Extension Publication) 388.