Installing XtraFinder (a free plug in to add functionality to Finder) solved this problem 100%. Did I mention that it is FREE?
In the settings there is an option to simply 'tick', which automatically adjusts the columns widths to fit the window size. It also allows the user to specify a given width for the Names column.
https://www.trankynam.com/xtrafinder/
Summary of Failed attempts (Mavericks):
Readjusting the size of the columns manually (holding the 'alt' key or not!) does have persistence, like people have mentioned, but only for THAT specific folder where you have adjusted it, so any new folders you make or folders that you haven't visited before still have the default column widths that are too wide.
I noticed this problem started for me when I used a montor with a much higher resolution than my MBP.
I have played around with the 'com.apple.finder.plist' file found in "/Users/your_user_name/Library/Preferences/", because this file should dictate the default columns widths and other parameters, however Finder appears have the incorrect values cached, or at least isn't paying attention to that file.
I did try deleting all the hidden '.DS_Store' files for every folder before too, but that also failed.