Increasing amplifier power to increase sound level
3dB is a doubling of the power as expressed in decibels.

Decibels are a logarithmic representation.  As such, it "compresses" the numeric difference.  The log of 10 to the base of 10 is 1.  The log of 100 to the base of 10 is 2.  So, you have a ratio of 10, but a difference in the logarithm of only 1.  From 100 to 1000 is again a factor of 10, but the difference of the logarithms (2 to 3) is still just one.

So, yes, going from 1W to 2W is the same ratio as going from 1000W to 2000W.  In both cases, you are doubling the power.

Your ears also have a (sort of) logarithmic response.  It allows you to detect very quiet things, and very loud things.

Your nerves have a limited range of intensity they can convey.  If the sound intensity were transmitted linearly to the real loudness (simple proportion,) then you would have a much smaller range of volume that you could hear.  Say, maybe just quiet sounds, and loud sounds are just a mash.  Or, maybe just really loud sounds but you couldn't hear an animal sneaking up on you.

With the logarithmic response your ears have, you can hear very quiet things and very loud things.

The extended range comes at the cost of not being able to detect small changes very well.



Some numbers:

Human ears have a dynamic range of something like 130dB. That's a factor of over 3 million times.

Using a linear representation, your nerves would have to be capable of conveying a range of intensities from 1 to over 3 million.

As it is, you can't really detect differences smaller than about 3dB.  130dB/3dB gives you a range of intensities from 1 to about 43.

So, your nerves only have to deal with a range of around 40 intensities.

Much simpler to convey than over 3 million.