Do all objects get larger in an "expanding universe"?
It would, if there were no interactions.

However, everyday matter is held together by other kinds of forces (electromagnetic, mainly). These are quite strong, and any "stretching" of space will be counteracted by these forces "pulling" the atom/molecule/object back to its original size.

So the expansion of the universe only matters on the larger, cosmic scale, between objects like galaxies which are separated by a large enough distance that they don't affect each other too much, gravitationally speaking.