Surely I'm doing something wrong, but I can't find how to refit some fighters to an improved version of them (the tonnage difference is less than 1%). 
At the planet where the fighters are in orbit, I select one of the Repair shipyards, then select the task Refit or Auto Refit, but the lists in Refit From, Class and Ship Name are empty.
The other tasks work well.
What am I missing?
Repair shipyards cannot refit. Not sure if the fact that they show the option is a bug per se or just a leaky abstraction in the UI.
Thank you, nuclearslurpee!
"
Repair shipyards cannot refit.": my first error.

So, I have to use a military shipyard (obviously, a commercial one cannot work on a military project).
Currently, when I select Refit, my military SYs don't list the ship type I wish, but only the type that they can build and sometimes few others; therefore, I imagine I should retool the SY for the updated craft, before I can refit the old ships, isn't it?