Cells by nature are small because they have to be able to work with small chemical reactions.
A small cell allows easier and faster transport of materials into and out of the cell. A cell by itself is a membrane-bound shape that performs chemical activities. Therefore, they are almost useless without millions of other cells to help coordinate bodily activities. If large cells made up the muscles, for example, we would have little function because there would not be enough cells to make up the tissues and move the muscles.
I can assuredly tell you that we do have examples of cells that have grown too large in size. Plant cells, for instance, will burst if they swell with too much water. Animal cells will respond the same way.
If all of the cells in our body spontaneously enlarged, we would find ourselves needing much more energy throughout the day. Simply put, bigger mechanisms requires more energy. Smaller cells are very efficient not only because of their ability to work with small reactions, but also because their size conserves large amounts of energy.