I practice no-dig with hay, mostly, sometimes woodchips, as the mulch cover. It is too hot and dry here to use compost as the covering. I’ve tried that more than once and it simply isn’t successful here. Compost, when I have any, is always covered with hay.
My preferred cover is woodchip but it’s not easy to access where I am and is getting more expensive each year. Too many people have seen the Back to Eden movie! I have ready access to hay so that’s what I end up using mostly. I love the no-dig approach and would never consider going back. Quite apart from anything else, I’m simply getting too old to be digging garden beds!
If it were me, I’d simply cut down the weeds, cover with hay and take it from there. Good luck with whatever approach you choose.
