As with any other bare ground, mother wants it covered, the "weeds" are doing the job of erosion control.
Just chop them down when you plant or place a heavy mulch over them a few weeks prior to planting, then plant through the mulch.
Trees are best a few feet away from the base of a raised hugel so they won't topple when the hugel starts settling.
I have seen a lot of people use fresher cut wood to make their hugels where I live, this will work but it takes longer for them to start going strong.
The best wood to use is already rotting wood, this is because it will soak up water faster, hold it longer and there are already mycelium present within this type of wood which is a great thing for plant roots.
I usually make stuffing (filling gaps during the build) with what is termed "punky" wood which is wood that crumbles when you pick at it with your fingers. This stuff is super adsorbent and holds a lot of water.
I have one that is home to our Egyptian Walking Onions, they needed water once so far this year and that was after 1.5 months of no rain, an unusual occurrence in my area.
Maintenance consists of sink hole patching with soil, punky wood or
compost, keeping a cover crop on so no erosion occurs, If it needs more topper then I put on more compost and mulch. Those are about the extent of maintenance.
In my world, weeds = plants growing where I didn't want them to grow. I just use them as a cover crop and chop and drop them when I want to plant something there.
Redhawk