Decibels are not a linear measure of power, nor is our perception of loudness/volume linear. (For that matter, the amount of acoustic energy does not fall of linearly as one gets further from the source, either, but is proportional to the square of the distance.)
As a rough rule of thumb, somewhere around 10 dB or so difference is generally perceived as "twice as loud." A 3 dB difference is a little louder (despite being about twice the acoustic energy), 1 dB difference not very noticeable unless you're paying quite close attention.