I tried one on once at a hole-in-the-wall samurai museum in Tokyo. It was pretty hefty but very well-supported - my head didn't feel wobbly or strained.
It's one man's work of passion. When I went, it was quiet enough that an attendant guided us around the entire first floor personally. It's not exactly tiny, but it's just two narrow floors behind an unassuming frontage, and so a big change from the other (public) museums in Tokyo.
My interest is piqued.
I'm inferring that they're just very small museums? Do they have any essential characteristics?
Google isn't being very helpful.