Each of the current (Ohio built) Ithaca 37's still has its own dedicated frame. There is not much difference between the frames of the 20,16 and 12s, as they are all the same width. The difference is/was in the height of the receiver, as certain internal components are interchangeable, while others are gauge specific.
What added the weight to the current guns and the 16ga in particular (as opposed to the 16ga 37s you remember) is the barrel. The Ohio built barrels are made out of a thicker and heavier steel than the old ones.
Add in the fact that the Ohio built 16ga is built on a 3" length receiver, brings the weight up to what you see today.
In order to chamber 3" shells, the Ithaca receivers had to be lengthened 1/4". Only the 20 and 12 were redesigned. (back in the day) (caveat, I have not had the chance to hold a 16ga built after the change to physically verify this fact). (However, Ithaca Gun's website specifies Ohio built 16ga guns -vs- prior made 16ga guns for certain parts that would be affected by length).
The extra steel, in addition to a heavier barrel is what brought the 16ga up to it's current weight.
This is the reason that I have scavenged parts and built my own 16ga hunting guns. A person can do the same by finding an older 16ga with a serial nbr that is after 855,000. Then buy an Ohio built barrel. You would have the advantage of better steel but still have the benefits of a 2 3/4" receiver.
With that said, the Ohio built Ithaca 37's ARE really nice guns.
A friend of mine hunts with a recent production CZ 16ga SXS. I did not handle it, but visually it sure looks to have been built on its own frame. It is a very cool gun.