Remington really missed the boat when they developed the 16 gauge 870. They adapted the 12 gauge frame to accept 16 gauge ammo, so you wound up with a gun that weighs just about as much as a 12 gauge gun, but in a smaller gauge. It carries like a 12 gauge but has the ammo availability of a 16 gauge.
I'm not a pump guy, but the Winchester Model 12 is probably one of the best executions of a 16 gauge gun. They use the 20 gauge frame so the old saying "carries like a 20 and hits like a 12" is appropriate.
Funny thing is, Winchester also made 28 gauge Model 12s on the 20 gauge frame, so you could have very similar weight guns in 28, 20, or 16 gauge.
I believe the Ithaca Model 37s had their own 16 ga frame, but I could be wrong on this. I've handled a couple and they were light guns.