We need more clarification to help answer your question. Are you growing sweet corn at home, or are you operating a farm? (Farm operators should work with an Ag Agent in the local county Extension office.) What specific weeds have you had problems with growing alongside the corn? Herbicide choice will depend on the weed species present.

Miri

Thank you for the additional information. If the Roundup you're using contains glyphosate as the active ingredient (not all formulations by that brand do - some use other chemicals, which will be listed on the front of the label), then it is a non-selective systemic herbicide, which means that it kills just about any plant the spray contacts. It's absorbed by foliage and moved into roots, where it kills the whole plant about a week or so after application. Since it has to directly contact the plant in order to affect it, any weeds sprouting after the application is made will not be controlled, unless the Roundup product also contains a pre-emergent (a chemical that prevents seed germination).

Some herbicide ingredients are selective instead, which means they only affect certain groups of plants, such as broadleaf weeds growing among grasses (corn is a grass, even though most such herbicides are used on lawn grasses). 2,4-D falls into this category as a broadleaf-selective systemic that does not affect grasses. Depending on the species of weeds you have growing alongside the corn, different herbicides might be better-suited to controlling some of those weeds versus others. Unfortunately we can't guess as to what weeds have been problems in past years based on the description. You may be able to get the weeds identified (either from fresh samples or photos) by local Master Gardener volunteers, if they hold any plant clinics in an area convenient to you. You can inquire with your county MG coordinator, or check the map of plant clinics on the linked page.

Do you use any mulch around the corn plants after they have germinated? If not, using mulch could help reduce the weed presence considerably, though more so for new weeds that germinate this year than long-established perennial weeds. (Spot-treating any pre-exiting weeds that regrow is probably best done with herbicide if you can avoid contacting the corn. Not all herbicide formulations are labeled for use around food plants, so check the label for details about where it can be used.) Ideally, weed would be removed without chemicals by manually digging them out or cutting them down, but we realize this is not something everyone can keep up with. A mulch layer about 3 inches thick should suppress most weeds that would be germinating this year. Mulch materials could include shredded bark, pine bark nuggets, wood chips (in a bulk delivery, these can be quite cheap if sourced from a tree removal company), pine needles, straw, or a biodegradable paper-based version of landscape fabric. Synthetic landscape fabric may also work (with gaps or holes cut into it for the planting holes), though we don't know how much microplastic pollution they contribute to the environment and food crops.

We do not recommend plowing/tilling the planting site if you can avoid it, because doing so can worsen weed problems by bringing weed seeds to the correct soil depth for germination and by chopping perennial weeds into pieces that than can regrow into dozens more plants. Discing the soil is a less-disturbing method for loosening soil for planting with the seeding wheel, or working the soil with a broadfork or garden fork alone should suffice. If the weed problem continues to be too much to handle, consider moving the corn plot to another, new location (crop rotation) for a year or more to make it easier to eradicate the weeds in the current spot.

Miri