Famous provenance is surely "nice to have", and in case of a weapon of a famous person could indeed drive the price up a lot. This is more true for something belonging to a famous historical figure than coming from a certain collection, although the latter can be re-assuring for sure.
In general though, I think value is assessed best through looking at the following factors:
1. The item itself
Quality, condition, craftsmanship, aesthetic appeal.
2. Scarcity
How rare is a piece of comparable quality, condition, etc. How does it compare to similar weapons from this culture.
3. Popularity of the genre
How many collectors are actively collecting this genre.
Some examples:
There are many Japanese swords on the market that score high on all points under 1. Yet, because an estimated 2 million blades survive, they aren't exactly rare. So collectors can afford to be extremely picky, and they are. So many survived that even the popularity of Japanese arms doesn't help drive the prices up much for any but the very best examples.
Another example are good arms from Sri Lanka. Their craftsmanship is among the very best work produced in Asia. It's hard to find an item still in impeccable condition. And even then, there are not a lot of collectors focusing on this field so even very good pieces can still be had relatively cheap.
Some arms tend to be so rare that collectors aren't at all fussy about quality / condition, they are just glad to find a representative example, period. This is true for example about arms and armor from Korea.
Still, value in this field is highly subjective. I recently paid way too much for an arrow with a Manchu word on it. It's just a stick with feathers for most people, and it wasn't even in good condition. But it was the only one I've seen with a Manchu word on it in the decade of studying Manchu archery and collecting related items. So to me, and only me, it was a real treasure!
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