In any time-signature, beat one is emphasised.Often subtly,but still a little more than the other beats. In 4/4 beat 3 is, as you state, a bit louder than 2 and 4. In 6/8 beat 4 is a bit louder than 2,3,5&6. This is generally the way folks can 'feel' the beat. I'm talking general pop music here - listen to Stravinsky, et al, and it can all change.One rarely stays longer on beat 1 in a bar of any time signature.
Check out QUANTISING - in recordings, etc., artists do play a bit early or a bit late, often not on purpose ! Digital machines have the facility to move the 'bad' notes one way or another, by a selected amount, to be back in time.
Having said all of that, some songs, and some genres of music, will specifically push or pull each bar (lead obviously by beat 1 ) on purpose, to create a different feeling to the pieces - I suppose this is the very opposite to quantising. A drummer, for instance, may be asked to play a song 'on the beat','early', or 'late'.