The ears are called אזניים which clearly relates to a scale which is a מאזניים. What is the connection? Do we have a scale in our ears??
Rav Hirsch writes in his commentary on tehillim [5/2] that when one hears he "balances" the words to see if they make sense.
Today we know that the inner ear is made up of two components - the cochlea and the vestibular system. The cochlea is involved with hearing, while the vestibular system helps with balance. So it makes sense that the ear is the same word as a scale because they are both involved with balance.
