Ragweed (Ambrosia artemisiifolia) and pigweeds (Amaranthus spp.) are common plant pests in home gardens across the United States. Although they aren't difficult to control, it may take repeated effort year after year to safely remove these weeds from the garden. Usually, however, you can do so manually once you learn to identify the species.
The pigweeds are a group of 65 to 75 species, and include the plants commonly called waterhemps. The most common species is redroot pigweed (Amaranthus retroflexus), which has a long red taproot. Pigweeds are tall summer annuals, growing erect to anywhere between a few feet and 10 feet. Flowers tend to grow in spikes, with separate male and female flowers. Color of leaves, stems, flowers and roots ranges widely depending on species. Because pigweed likes to grow in open areas where there is ample sun, it often moves into gardens or agricultural settings.
In areas of the garden where you have a serious pigweed problem, space your plants close together. Often a dense cover over the soil where pigweed is trying to sprout can have a discouraging effect. You can mitigate its presence in gardens with heavy tilling in the springtime before you plant and in the fall when crops are finished. Moving your vegetables around each year discourages both weed and insect pests. If possible, identify and pull up pigweed before it has a chance to seed.
Unlike pigweed, there is only one species of ragweed. Its leaves are between 1 and 3 inches long and roughly egg-shaped in outline, though their leaves are very feathery and open in appearance. Leaves have fine hairs coating the upper surfaces. Stems also have rough hairs and are often purple rather than green once the plant matures. Ragweed flowers are yellow, blooming on long, spiked inflorescences. Native to North America, it too prefers disturbed sites such as gardens, orchards and roadsides.
One of the most effective approaches to ragweed control is to mow it. This exhausts the plant’s energy reserves and prevents it from producing seeds, of which a mature plant can produce 62,000 per year. Mow as close to the ground as possible, but only before seeds are formed, as afterward this will likely result in helping the plant distribute seed. You can also pull ragweed up by hand, though again, do so before seeds mature so that you don't unwittingly spread the plant’s seed for it.