Down or synthetic, belay jackets were standard issue LONG before Twight was a name anyone knew.
Climbing you almost always wear a puffy over your outer layer because you’re wearing a harness, which always goes over your outer layer. Taking the outer layer off to get a puffy underneath would necessitate taking the harness off, or at a minimum loosening it enough to rearrange whats under it. You’re literally hanging your ass into outer space hundreds of feet off the ground, so taking your harness off is something you dont do without a great deal of forethought. Then as soon as you’re climbing again you take the puffy off, so you’d end up repeating that many times a day. Consequently I think its fair to say that a “belay jacket” is pretty much always worn over your outer layer.
I rarely wear a heavier down jacket under an outer layer. I have a 6oz 900 fill down jacket that I wear under sometimes. Its very warm, it compresses a little but is still quite warm. About the only reason I wear it underneath is to either protect the fabric from tears because I’m moving through brush very slowly and chilled, it’s screaming cold and I don’t want to trash my expensive down jacket; or because I am archery hunting from a tree stand and the down fabric is loud so I wear a soft shell over it in order to be quieter drawing the bow. I use a midweight puffy as a mid layer pretty frequently, something like 2.5-3 ounces of down fill or less, that’s a great mid layer for very cold temps that is extremely packable and also functions as an outer layer if I don’t need the shell. It’s still much warmer than most mid layers, and it’s much more packable and lighter than any mid layers that would be as warm, so I don’t really see this as an active insulation layer as much as simply a versatile insulation layer.
Also if its cold enough to really need a heavy puffy, liquid water generally freezes onto the outside of the fabric before it has a chance to saturate the insulation hardly at all. Climbing, that happens when an ice climb is gushing water even though it’s only five or 10°F, and the wind is blowing the spray onto you. You can shake the ice off when you shed the jacket to climb, and youd be surprised how much water you can sit under and keep it dry. Generally the water is going to come from the ice thats frozen to the outside of your shell, where it’s going to melt when you cover it with the puffy—that is the reason for some people preferring synthetic. In that case wearing down underneath would be great, but there’s that harness issue again. (Not to mention getting a freezing shower when you take your shell off). Luckily when hunting that’s not so much of a problem. I don’t stand under gushing frozen waterfalls when I’m hunting, so in temps when I’m wearing a jacket that heavy the precip is usually already frozen. That means when I pull it on over an outer layer Im not covered in ice that is going to melt. It’s pretty easy ime to stay dry in those conditions. Its temps rigjt around freezing when water ISNT freezing that are more difficult. In my experience in those conditions, it’s not so much about the amount of insulation, as it is about managing moisture. To me the puffy under the shell thing is for situations where that makes more sense for managing moisture, as much as it is about it managing heat better.