They’re designed for the seat to be sat on. It’s not so much the weight, but where it is, like you said. Not even the properties of the surface you’d be standing on, but that it’s the part not over anything. It’ll cause some rotation-y force the toilet isn’t designed to handle.

If you have a ruler that’s half on a table and half hanging off, it doesn’t matter if you put an empty cup or a cup full of water on the side that’s on the table, it isn’t likely to fall. Likewise, if you put an empty or full cup on the end hanging off the table, the ruler will fall.