I also think that you should put the unit of measure after the word one, but I'll leave it out in this analysis.
All items have weight one.
All items have weights one.
All items have the weight one.
If you are trying to say here that each individual item in a set weighs one, you would say "Each item has a weight of one" or "all the items have a weight of one." The latter is a bit ambiguous, though, since it could mean that all the items taken together have a weight of one as well.
The weight of all items is one.
This would mean that the total weight of all items in existence is one. "The weight of all the items is one" means that all the items taken together weigh one. "The weight of each item is one" means that every item in the set weighs one.
The weights of all items are one.
As above, this means all items in existence. However, now you are (probably) saying that every individual item in existence weighs one. More correct would be to say "The weight of every item is one" if you wished to convey this idea.
All items weights are one.
All items' weight is one.
These are both grammatically wrong. The grammatically correct sentence is "All items' weights are one." The meaning is the same as "The weights of all items are one" and my comment there applies here.
Now, I would say "Each item weighs one" to mean that every individual item weighs one, and "All the items together weigh one" to mean that the total weight of all the items is one.