With few exceptions, the most aggressively invasive weeds here are exotic. In other words, they are not native. They came from other regions where they were likely compliant participants of their respective ecosystems. At home, where they must compete with other members of their ecosystem, they may not be so aggressively invasive. Ecology is the opposite of a home field advantage.
Exotic species become invasive weeds in foreign ecosystems for a variety of reasons. For some, the climate is more favorable. Some grow and proliferate more freely without diseases, insects and animals that troubled them back home. There are also several that simply compete more aggressively for space and resources than native species are accustomed to. It is a jungle out there.
Most invasive exotic species are annuals. Many are biennials or perennials. Some are vines, shrubs or even trees. Most were imported intentionally, for a variety of reasons, and then naturalized. Forage and cover crops were some of the earliest of exotic species to become invasive. Other invasive species escaped from home gardens. Blue gum eucalyptus was imported for wood pulp.
Regardless of their origins or physiological forms, invasive species are weeds. They compete for the same resources that desirable plants use. They impede on the aesthetic appeal of gardens and landscapes. Some types of weeds become hazardously combustible. Even if not directly problematic, invasive weeds disperse seed that can be problematic nearby. Many disperse stolons.
Most weeds start early and grow fast to get ahead of their competition. They are more active at this time of year than at any other time. They are also vulnerable. While the soil remains damp from winter rain, they are relatively easy to pull intact. They have not yet dispersed seed for their subsequent generation. Later, they are likely to leave behind seed and bits of roots that can regenerate.
It is important to pull or grub out seedlings of unwanted shrubbery and trees, as annual weeds. They are likely to regenerate if merely cut.