Think about the weed seedbank, which is the reservoir of viable weed seeds held within the soil profile of an ecosystem. These seeds may be recent additions (e.g. seed that was produced on mother plants within the previous year) or else dormant seeds that have persisted in the soil environment across multiple seasons (e.g. seeds that have not germinated despite exposure to optimal environmental conditions).
Whether we realize it or not, our ability to manage weeds in agricultural or horticultural settings can be significantly influenced by the density and diversity of the weeds seedbank. Numerous studies have demonstrated that as weed seed numbers increase, so do the numbers of weeds that survive management strategies (Diehlman et al. 1999; Hartzler and Roth 1993; Sparks et al. 2003; Taylor and Hartzler 2000). In other words, the greater the number of seeds in the seedbank, the greater the number of weeds that may emerge and the greater the number of plants that may escape chemical or cultural control practices.
I am willing to argue that high density seedbanks may facilitate the development of herbicide resistances because where weed infestations are heavy, the probability of for selecting resistance can be high, even if the mutation rate is low (Jasieniuk et al. 1996).
So, how do we specifically target the seedbank for weed control? One strategy is to increase seed mortality. Seeds are not impervious to decay and damage; pathogens can colonize seeds in the soil whereas birds, small rodents and insects will feed upon them. Studies have shown that farm-level management practices (e.g. tillage, crop selection, cover cropping, pesticide use) can affect weed seed predation (Menalled et al. 2006), although landscape level factors (e.g.habitat diversity, predator diversity) ultimately influence in-field seed survival, as well (Trichard et al. 2013).
Another method is to manipulate seed germination and seedling emergence. Deep tillage can bury seeds below their optimal germination zone. On the other hand, cultivation can stimulate seeds to germinate. Growers may utilize stale- or false-seedbeads, wherein a field site is physically prepared (but planting delayed), to encourage weed emergence; seedlings, which are susceptible to control efforts, may then be sprayed with a herbicide, flamed or else cultivated (Lonsbary et al. 2003).
One of the best ways to reduce the size of the seedbank? Don't let seed return to the soil. Your grandmother was spot on: 'One year of seeding means many years of weeding'. Prevention can assume many forms: handweeding, cleaning equipment between fields, planting weed free seed, mowing weeds prior before flowering, being mindful of your mulch and manure, and screening irrigation water to prevent seed immigration. And not just during the cropping season. Pre- and post-harvest weed management can also influence the size of the seedbank.
Weeds will always find a way into your field (for instance, you can't stop the wind from blowing), but you can maximize the impact that the seedbank has on your (current and future) level(s) of weed control. The ultimate goal of weed control is to protect this year's yields AND to try and reduce pest densities in your coming crops.