What is the value of a 1935 Browning Sweet Sixteen?

Not all 16ga Auto-5 shotguns are Sweet Sixteens. That is a specific lightweight model that was introduced in 1936. Chances are you have a standard weight Auto-5 in 16 gauge. Either way, it originally had a 2 9/16" chamber and is not suitable for modern 2 3/4" ammunition unless it has been modified for the longer shell. Value depends on condition. Anywhere from $350-$1000.