In Memory...

Choose Cell Notebook History and open the Cell Statistics section. Content bytes gives the memory used to store cell expressions. Total bytes includes memory used for cell labels, cell tags, etc.:

  • Cell Statistics does not include memory used for non-cell notebook data.
  • Memory usage shown in Cell Statistics does not include memory used by the kernel to store input expressions and the results of evaluations.

In Storage...

Get the size of a notebook file with FileSize:

Use ByteCount to find the amount of memory used by an expression in the kernel. The value returned is the memory occupied by the argument expression after evaluation:
The approximate total memory footprint of a notebook can be calculated by evaluating MemoryInUse[$FrontEnd] before and after opening a notebook:
Since the memory figures may include memory used or freed by front end processes other than those associated with the notebook, the calculated usage is not exact.