Well - the sound of a guitar comes from three things, the vibration of the strings, the vibration of the guitar body (mainly the top) and the vibration of the air in the body cavity which in turn is partly caused by the vibration of the body and partly by the excitation of the air by the strings in front of the soundhole (a little bit like blowing across the top of a bottle. Next time you have the strings off, try three things - tap the bridge and listen to the pitch of the resulting sound, put a tuning fork on the bridge and listen to there the sound comes from, and sing into the soundhole and listen to the resulting sound.

Now, the teoretical maximum amplitude (ie loudness) of the sound from the strings is limited by how big the vibrations that they make are. Hit a string too hard (I often do) and the strings hit the fretboard which immediately reduces the amplitude of the fundamental frequency of the string to the height of the action at the mid-point of the string. So too low an action will in fact make the guitar quieter. Many of us will have experienced this as a guitar has aged and lost its sound - only to have it miraculously revived by a good refret and setup.

Next, what causes body vibration? Two things (mainly). The in and out pressure on the saddle caused by the string vibration and the twist in the top caused by the tension in the string. Both of those forces are greater the tighter and heavier the string (but overdo it and the guitar is hard too play and overdo it too much and you can twist the top or even break the guitar in half). The lighter the strings the less they can make the top move.

If you are a reasonably experienced player, with no hand problems, and the guitar is well set up you will get a bigger, rounder, more responsive sound by playing 12-53s or 12-56s than 11-49s ("lights" - usually, but string brands vary) or even 13-56s or 12-58s (if your guitar will stand it, some were not designed to take it). Back in the 60s 13-56s were the norm, but many players today use 12s in stead. I nearly wrecked my Mugen THE-78 by playing 13-58s on it, but it sounded huge!

So, chicken and egg, some manufacturers have lightened their tops and bracing, so that bodies move more, and produce more sound...

If your guitar action is too high, fretting the strings will pull the guitar further out of tune, and you will notice this more the lighter the string. The forward progression (or relief) of the neck should not usually be more than 0.25mm. I play 2.7(bass) - 1.9 (treble) action at the octave, a bit less on a 12-string. There is only one right height for the action at the first fret - it is so that the action at the first fret is the same as it is at the second fret if you put a capo on the first fret. If your guitar is set up like this you should find that you are not pulling it out of tune when playing.