Most of my knitting with thin yarn is for socks. I use the size needle that gives me the desired fabric at a tight gauge. I couldn’t say what is suggested on the label, I just don’t think about it. If I’m using the yarn for other than socks I just try different needle sizes until I like the results.
Since I don’t follow patterns religiously and ‘make it up as I go’ my actual gauge isn’t that important. That’s why I do toe-up, knit to fit socks. I use the number of stitches that works with the yarn and needles I want and don’t have to do math to figure it out. I just increase until the size is right for the intended foot.
The socks I mentioned above got frogged. I don’t have the right needles to make working with the yarn easy enough for what I was doing so I started over with different yarn from a frogged project. I think it’s sport weight and I’m using a US1/2.25mm circ. I made wrist warmers from the same yarn and think I used US3/3.25mm needles. If I knew what the yarn is I could look it up. Maybe it’s dk weight.