The set of sixteen items below can be partitioned. Each partition is of four items that have something in common. I invite you to figure out the partitions and commonalities. You'll find that the four commonalities are of the same type in some sense; and that, taken together, they clue an eight-letter word.
BULL, COME, DICK, KO, LEE, ME, MULL, NIT, RE-ROBE, RICH, RUBBLE, SEW, SHELLS, STIR, TELL, WEIGH
Hint (added later):
RE would work instead of RE-ROBE (and would be a more appropriate word for this puzzle) were it not for the fact that it's also a musical note. I included RE-ROBE because it's easy and in my hope that people use it to start solving the puzzle.
Another hint (added even later):
I don't know why I included NIT rather than KNIT. It makes no difference whatsoever.
Another hint (added even later):
LEE and TELL are in the same partition.
Another hint (mentioned a little while ago in the comments on the question):
Bubbler asked me whether the KO on the board is "ko" or "K.O." and I replied that it's the former and that that question is important.
Another hint (mentioned a little while ago in the comments on an answer):
The fact that none of the words contain the letter A is just by chance.
Well… there may actually be some sort of linguistic connection between the wall's rules and the absence of an A. Like, maybe it's easier to find non-A words to fit the wall's rules than to find A words to fit them. But knowing that is probably not going to help you.
Another hint (added even later):
One European and one African country are represented here by name.
Another hint (added even later):
Also, a big city in East Anglia is represented by name.