"3) In order to "simulate" the human perception, there are some standard ways to filter the signal that a microphone is able to grab. Some standards give more "weight" or importance to a range of frequencies, others to a different range, they can use different slopes when filtering, ... and this is what weighting means."

Yes, that's the "weighting" I was referring to.

"2) Humans have different sensitivities(perception) for different signals, the main parameters being amplitude and frequency."

Note that the sensitivities change somewhat with the sound level - that's why there are different weighting scales: some are used for quieter sounds; others for louder sounds.
It's up to the user of the instrument to use an appropriate measurement.