Run a File Size Report
This won't list everything, but instead quickly shows you the largest assets stored in your Asset Bank.
As an administrator, navigate to Admin > Reports and select the Asset tab.
Under All Items by Date and/or File Size build the report by specifying a date range by upload or modification date, and a threshold file size (for example, files over 10MB in size).
Click Get Report to run the report.
On the results page you have the option to save a list of the assets to an Excel spreadsheet.
Advanced Search and metadata export
Using this method, you can list every asset in your Asset Bank in an exported file, which also lists the file size of your assets.
Choose Advanced Search and in the search options select all Access Levels (this will return all assets).
Run the search.
On the results page, choose More Actions > Export all results... and ensure Export asset files is un-ticked, you may choose to export as a native Excel document.
Click Run Export to export the metadata, then download the exported file manually by clicking on the filename which appears on the next page.