If the gun is from the 40s, it is not a Sweet Sixteen. If it is from the early 50s it might be, Sweet Sixteens were introduced in the early 1950s. Sweet Sixteens are actually roll-marked "Sweet Sixteen", and are not the same as a standard 16 ga A5, although a lot of people like to think so because it sounds kinda catchy. Sweet Sixteens had vent rib, gold trigger. There are a lot of standard 16 ga that get advertised as Sweet Sixteens that are not, as said above. The reason they were called Sweet Sixteens was that they were a 16 ga built on a light 20 ga frame instead of a 12 ga frame, which was common practice years ago.
Browning Arms Co never made their own guns (Browning Brothers did, but that ended in 1883), they were made by other firms to Browning specs and sold by Browning. Browning Arms has been located in several cities over the years, most notably St Louis, MO and Ogden, Ut.