I don't know your particular mixer, and you didn't say which model it is so I can't go look it up on line. But if the channel gain increases when you turn the knob from -16 to -60, then maybe those numbers express the signal level (in dBu or dBV) at the microphone input which should produce some nominal level in a channel with that setting. In other (and fewer) words, it sets the sensitivity level of the microphone input.
For example, I noticed that someone in the Yard Sale is offering a pair of Audio-Technica AT3035 microphones. If you go to Audio-Technica's Web site you can find this specification for them:
OPEN CIRCUIT SENSITIVITY .... -32 dB (25.1 mV) re 1V at 1 Pa
So maybe the idea is that knowing the above specification, you would set the trim pot to -32 on any channel where you're connecting an AT3035, and so on. If that's the intended logic, and if that procedure is carefully followed, it would make the "0" fader setting on every input channel correspond to the same sound pressure level, regardless of what type of microphone is on the channel.
However, that's just an inference; like you, I'm much more used to the Mackie type of arrangement in which the dB number on the trim pot tells you the nominal gain setting of the input stage, and turning any kind of volume knob clockwise makes things louder, not softer. The Yamaha arrangement, if I've correctly guessed (whoops, I mean "inferred") what it's about, sounds like someone in the marketing department's Absolutely Brilliant Idea--for which they should be duly rewarded by keeping them the hell away from any product design ever again. On equipment to be used for live recording, where you don't normally get a second take, any controls that work the exact opposite of the way most users would expect them to work are not a welcome innovation in my book.
--best regards