Well, we need to consider Newtons Third;
If Body A exerts a force on Body B, Body B will exert a force equal to the initial force and opposite to the initial forces direction. I reformed it a little just to make it clear on how this situation may go.
So, Body A being me, and Body B being my wooden floor that my cats dropped a deuce on the one time I let them in my room.
My weight is the force that pushes on the floor, body B, and the floor exerts a force back on me, Body A, the reaction force. The object may itself not budge, but an object doesn't need to necessarily budge, as long as you exert a force on the object the object by Newtons Third must exert a force back on the you, the body that exerted that force.
As for the answer to your question, I'm no chemist, or molecular fellow (I didn't do it, Physics and Biology xD) but all the atoms exert inter-molecular forces that prevent them from moving around too much, they're held in some sort of structure. If you exert a force, you push on that structure, putting shear and/or tension in to it. If you were big enough, the floor would break, after all the bonds wouldn't be able to handle your huge bum anymore (I hope that isn't the case!).
You can see where I'm coming from. The floor may bend ever so slightly, or it may compress a little, but in the end all this action results in a force being exerted back on you, the person who (hopefully) wont break through their ceiling
