I garden a sand/gravel mix. Burying grasses is of now value as too many roots and seeds to germinate. I mulch garden with straw and that has little affect on grasses. What I should do, I won’t.
if you could do what i do you'd find quite an improvement.
i dig trenches about a foot and a half and then scrape the surface and as many roots of the weeds as i can into the bottom of that trench. and then i put down some cardboard or newspaper over that and bury it. very little of that will come up again. it works.
as for once you have it cleared and want to keep it clear, keep hitting it with a strap hoe before the weeds have much chance to grow, spread roots and seeds around. if you are consistent enough you can manage a half acre of gardens without that much effort.
in the early fall, if you can turn under the garden and plant winter rye or winter wheat that will give any weeds competition and you won't have such a problem in the spring. turn it all under in the spring again several weeks before you have to plant.
yes, i know, i do these things in a lot of gardens with a lot of things in the way. if i had one half acre of open ground that i didn't have to go around all this stuff i could cut my time down to about 1/4 of what i currently spend. so perhaps i could manage a whole acre? dunno, never been able to do what i want.
still i know these methods will work as i use them all the time.
yesterday i put up one garden of 200sq ft in less than an hour. some weeds, there always are, but i didn't have to dig up or turn the whole garden. just dig one trench and bury all the garden debris plus some weeds and the neighboring cosmos after i'd harvested the seeds.