The Sweet 16 does not date back to the early 1900s...

I'm only guessing at this, but I would expect the light Browning 16 gauge ( Sweet 16) may have first been produced in the late 40s at the earliest, more likely the early 50s..

The Browning A-5 does date back to near 1900, but he patent was sold to Remington, who manufactured it as the Remington 11 for quite a few years, I believe until the late 40s..

After the patent expired, Browning ( in Belgium) began to produce the A-5 under thier own name again.. It was made in 16 gauge, but I believe the lightweight versions of the A-5 ( Light 20, Sweet 16, light Twelve) did not come along until around 1950, give or take a few years..