There is no such sorting option available.But you can create a Smart Collection that will help you to organize images according to their file size.Technically its not "sorting" your photos, it is filtering your photos.
Please let us know if it helps.
Thanks. This is not what I'm looking for, unfortunately. I am really surprised that such a simple sort job is not available. The scenario is: I have the exact same photos in my library since some photos got added through camera syncs on top of email downloads etc. Hence, I want to be able to look at the pictures in grid view next to each other and discard the duplicates. File names and other metadata are likely to be different, hence the need for a visual check. Bracketing photos by file size will not help in this case.
The best you can do in LR without plugins is to search by a particular size bucket, as discussed above. You could add your vote and opinion to this topic in the official Adobe feedback forum: Lightroom: Why can't I sort by image size and dimension like Bridge does...or have I missed something obvious? (This forum here is primarily a user-to-user forum in which Adobe product developers rarely participate.)
Meanwhile, if you want to get work done, you could consider plugins. Laura Shoe recommends Find and Eliminate Duplicate Images in Lightroom | Laura Shoe's Lightroom Training, Tutorials and Tips, though I've seen reports from others that the plugin doesn't appear to be supported any more. The Data Explorer plugin will bucket photos by file size into collections (but not actually sort), making it easier perhaps to see visually similar photos, depending on how many you have. The List View plugin can export files and their sizes to Excel, where you could message the data to let you sort by size numerically (the plugin uses a text sort that doesn't properly handle numeric fields).