Weeds are generally a sign that your ph or other soil components are out of wack relative to what's optimal for grass. In the case of weeds growing through gravel.....it's 'cause they can and will. Any glyphosate will take care of that. Eraser is about half the cost of Roundup and it works the same.
Agri Star (among others) makes generic versions of most popular weed killers and they cost about half of the brand name. In many cases though you still need a license to buy them. Tractor Supply sells Pasture Pro (2,4,D) by the quart and you can buy it without a license (but you need a license to buy a 2 1/2 gal. jug). There aren't any grazing restrictions for 2,4,D so you don't have to worry about your pets. My barn cats and dog go in my fields after I spray with no ill effects that I've ever seen.
If you keep your soil in balance and mowed you'll have a lot less weeds.