
I can't speak for the Japanese teaware; but, believe it or not, your new duanni (I have the same one) is actually considered to be on the *large* side for a one-person yixing pot!
It's designed for a Chinese brewing style called "gongfu" which you can read about all over this site if you do a little searching. The basic idea is that you can keep brewing a good oolong over and over (and over!) again. Each steep will bring out different tastes and qualities. 8 steeps in a 4 oz pot is a litre of tea, so you do end up drinking just as much or more than you would otherwise. You get a much more interesting experience than you would out of one big mug full of oolong.
To make this work, you use lots of leaves (enough to fill at least 1/4 of the pot, but many people use more), water straight off the boil, and really short steeps of about 20 seconds to a minute. The exact amounts, temperatures, and times depend on the individual tea and your own preferences, but part of the fun is figuring it out as you go.
I was surprised at how small my first yixing was when I got it; now it's WAY too big—and I'm even finding my 4.2 oz duanni rather spacious.