The Sweet 16 started being produced in 1936 as the lighter weight version of the Standard weight 16 ga. A-5. The "Sweet Sixteen" engraved on the action didn't appear until around 1953. However, the pre-1953 16 ga lightweight guns had a gold plated trigger and an engraved receiver. The Standard weight guns had neither for the entire production run. The Sweet 16 was advertised to be "around" 6 3/4 pounds with a plain barrel. The problem with identifying which is which by weight is that the difference is only about 4 ounces. So a sweet 16 with a 28" barrel is probably the same weight as a standard weight gun with a 26" barrel. Add a rib to the barrel and the "lighter" gun becomes heavier than standard. Also, the Standard weight gun was advertised as "around" 6 3/4 lbs. I have noticed that the barrel ring on Sweet sixteens usually has a series of holes drilled in it. This accounts for some, but certainly not all the difference in weight. The Sweet 16 will have a letter R as part of the serial number and the Standard will have an S. Again, no help in differentiating because the letter codes started in '53 along with the "Sweet Sixteen" label. Prior to '53 the serial numbers are all lumped together for LW and Standard 16's.
And I'm not a Browning expert. I just happened to have the Browning book ready to hand.
Also keep in mind that to most people a 16 ga A-5 is a Sweet Sixteen. Period. I've never noticed a significant gain in value for a "Sweet" gun as most Standard guns are advertised as Sweets 16's and considering the small (and questionable) difference in weight that makes sense. The only way to guarantee the difference is to have a post-53 gun that has the appropriate engraving.
Best
Nick