you could just hoe and rake off the weeds each week but only to the depth of the rake ...DO NOT disturb any deeper . That way all the weed seed in the top 3" will germinate and after a few weeks no more seeds to germinate...I have done this many times and it does work ...there are only so many weed seeds there to germinate . Let them do so, then hoe and rake off , let them germinate again , hoe and rake off , but don't go any deeper than the the rake teeth. I really do not understand the reasoning behind mulching forever, it leaves ALL the weed seeds there to germinate at the first opportunity they get. Each to their own and all that , but it is so much easier to hoe and rake once a week till they are all gone from the top 3" or so . Why try to fight them ... let them germinate, hoe them , then rake them off simple ....What this is mainly I think, is people have forgotten how to manage veggie plots . They have got used to just spraying everything in sight with weed killer and not doing the basics of ground clearing . Mulching will not cure the problem of weeds , it will only cover them , they are still there !!! Bindweed , dock , dandelion etc have to be dug up , but weed seeds HAVE to be allowed to germinate , otherwise they remain in situ.
Hoeing and raking is part and parcel of gardening , and is very quick unless you are doing 1/2 an acre or more. You can even just rake any bare ground with germinated weeds on hot sunny days and the sun will kill those lifted . Do that every other day , it takes just a few minutes, and in no time no more weeds....You just have to remember not to bring up any soil from below the cleared top few inches. Been doing this for 40 odd years now and it works folks, it is just using nature and the weather. Very simple , easy to do , free, and eco friendly , it is also the way it has been done since man has toiled the earth, why try to change it ? work with it !! You won't beat it !! This isn't a rant or a moan , as I say everyone does things their own way , this is mine and it was everybodies not that long ago .
cheers
Russ