Would insulation add too much weight onto an old plaster ceiling?

Do any of you have experience with plaster ceilings???

I live in a 1930's house, and all the exterior walls seem to be well insulated, but for some reason the builder never put it in the attic spaces.

I do know the person who built it was an engineer, and him and a bunch of friends in the construction industry put in a little effort... so I would think they did things for a reason.  Since they insulated the exterior walls, I wonder why they didn't insulate above the ceilings?

Now I want to insulate it. But the question which is hanging over my head is - did they avoid insulating the ceilings because it would add too much weight to plaster?  And were they afraid that extra weight would eventually make the plaster fall?  I've heard some horror stories about plaster ceilings falling and hurting people.