Road noise reduction in the balcony
Different sound frequencies have very different characteristics in terms of what you can do and how effective it will be.  The road noise is a mixture of sound frequencies.  There probably is nothing practical you can do about the low frequency noise, but you might be able to muffle the sound a little by reflecting high frequencies and absorbing mid frequencies.

Think in terms of the sound panels used to create cubicles to reduce office noise.  They aren't real effective, but they help a little.  You could even start by experimenting with ones you find in a used office equipment store.  You could also make your own.  Plywood with thick carpet padding glued on, and a protective cover would be a reasonable first test.  But making either of these weatherproof will be a challenge.  

For more naturally weatherproof materials, you could look at T1-11, thick, dense styrofoam panels, or even corrugated plastic panels for the backing, and closed-cell foam sheets (the material used for boating applications) for sound absorption.

Of course those would totally block your view.  If you have a lot of money to blow, you could try clear Lexan panels.