For on premises versions prior to 2016 the file size limitation comes from SharePoint. It imposes a maximum file size of 2 gigabytes per file.
For SharePoint 2016 and Office 365, the maximum file size has been increased to 10 gigabytes.
In SharePoint 2016, you will need to manually edit the web application where your site collection resides. There is a setting that limits the size of file you can uploads and, by default, the size is much less than 10 gigabytes. Then, you can manually upload the files to SharePoint with your browser, and then use Sharegate's Bulk Metadata Editor feature in order to manually set the fields values.