I agree with mulching. I worry about extending my garden beds due to the wild violets. We managed to pull the bulk out of the front bed, but it took an entire summer. My in-laws were visiting and bored during the day so would go out and dig down to the roots. They are persistent buggers! I have followed up this year by putting a second layer of thick mulch and taking any foliage off in order to starve the roots. Beside the stray leaf and weeding a lot before the mulch was put down, I have barely needed to weed. Whatever does grow through is weakened by having to push through the mulch. My lawn is almost 100% weeds dispite reseeding every Spring and Fall. I am planning on reseeding the lawn soon for the fall and then placing the feed pellets as an organic preemergent in the Spring. Might help with the garden, too if the lawn stops being one huge weed.... :)

The World Health Organization has declared glyphosate products to be potential carcinogens and numerous studies have found this product is much more persistent than the manufacturers have told us and it is found in numerous food products. Using glyphosate products is then hazardous to your health as well as the health of everyone else in the world. A more environmentally sound method of eliminating this invasive Mulberry is to cut it down and keep any new growth cut so that new growth does not feed the roots of the plant. kimmq is kimmsr

No clue what it is but for woody stuff like that try a triclopyr-based herbicide like Weed-B-Gon Chickweed Clover and Oxalis.

Likely this one: https://www.bing.com/images/search?q=echinochloa+crus-galli&qpvt=echinochloa+crus-galli&form=IARRSM&first=1&scenario=ImageBasicHover