Dogs like a little variety and they know the value of adding some greens to their diets. They are actually omnivores which means they eat meat and vegetation..not to mention kibble from any available cat bowl, table scraps from the kitchen garbage can, and all sorts of other things at which humans turn up their noses.
Some dogs frequently eat grass and don't throw up afterwards. They may simply like the taste and feel the need to add some roughage to their regular meals. This pertains more to those dogs who actually chew and swallow the grass blades thoroughly. Grass can also act as a healthful aid for dogs with upset stomachs who need to purge their systems. In that case, you might notice that they seem to almost gobble the grass without really chewing the blades. The prickly little stalks irritate their stomach linings and cause them to vomit.
Grass is fine for dogs when it is free of pesticides, lawn chemicals or other harmful substances. I recommend that you grow a container of grass for your dog to nibble on indoors or provide her with a patch of special greens in the backyard. You will be offering food that offers certain vitamins, minerals and fiber not found in the kibble in her food bowl. And don't forget to entice her taste buds by adding some cooked or raw veggies, such as green beans or carrots to his bowl from time to time too.
As for dog friendly weed killer...my favorite is simple bleach. Most times, dousing a weed with bleach will kill it, and won't hurt your dog.
I hope his helps.