Dust,
A level meter won't tell anything if a speaker has a mechanical problem. Also, if the problem is caused by the amplifier, then you won't know what is a "good" or "bad" meter reading.
Since you have only one speaker that is messed-up, then you probably have another one that is good. Swap the 2 speakers, and if the messed-up problem moves to the other side, then that speaker, not the amplifier, is messed-up. If the problem remains on that same side, then the amplifier or the speaker's wiring (in a car) is messed-up.