You can use eco friendly weed killer or you can pull them by hand. If the ground is clean underneath prior to spreading the gravel then it is pretty easy to just pluck stray weeds here and there. For the most part once it has been on the ground for a while and kept weed free they just stop growing. You wipe out the roots left behind when preparing the ground for the gravel.

We are on an acreage so the surrounding grass is full of dandelions and thistle. I have gravel but I am going to get rid of it. I can't compete with all the weeds that grow in it. Maybe the size of the gravel helps?

Roundup is the answer.

Please note that if you are planning to have this aas an organic garden you will want o stay away from Roundup. Roundup is produced by Mo Mansanto. They are the largest producers of GMO. You may risk cross contamination by using this product.

Roundup becomes inert when it enters the soil. Don't be afraid of it. Just because it's a weed killer, that doesn't automatically make it bad. It's a sodium based product. And no, I don't work for roundup. I have a very large yard and have been using roundup for years. Just don't spray any broadleaf plants that you don't want to get rid of.

Glyphosate is not an inert ingredient.

After researching glyphosate and the meaning of the word inert, I'll stick with my assessment of roundup.

You can use a flamethrower on gravel. Very easy and fun!

You could try using landscaping paper under the gravel. We did and then compacted stone dust between the raised beds. It compacts into a hard surface, more difficult for weeds to penetrate. It has worked well so far and looks very nice.

I sprinkle water conditioner salt on my gravel to keep weeds from growing. The flame thrower works well to kill weeds, as does vinegar on a dry day.

Just bend down and pull them when the soil is damp underneath. Most will pull right out and you won't have put any chemicals into the soil (yes, vinegar and salt are natural but they won't help the soil any). Bonus: You will get a bit of exercise without having to pay a gym membership!

What about putting a pond liner?

Jeffasby,
Glycophosphate binds with the soil. It does not magically become inactive. It has finally been categorized as a carcinogen. https://ehjournal.biomedcentral.com/articles/10.1186/s12940-016-0117-0
The other problem with RoundUp I've known about for years are the inert ingredients: https://www.scientificamerican.com/article/weed-whacking-herbicide-p/